University of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401$1$-Absorbing prime property in lattices114818310.22124/jart.2024.28061.1693ENSh.Ebrahimi AtaniDepartment of Pure Mathematics, University of Guilan, Rasht, Iran0009-0001-2215-9640Journal Article20240731Let $\pounds$ be a bounded distributive lattice. Following the concept of $1$-absorbing prime ideal, we define $1$-absorbing prime filters of $\pounds$. A proper filter $F$ of $\pounds$ is called $1$-absorbing prime filter of $\pounds$ if whenever non-zero elements $a, b, c \in \pounds$ and $a \vee b \vee c \in F$, then either $a \vee b \in F$ or $c \in F$. We will make an intensive investigate the basic properties and possible structures of these filters.https://jart.guilan.ac.ir/article_8183_3757f4baa8dda28f3be387e4996cd263.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401An introduction to bipolar fuzzy soft hypervector spaces1535884610.22124/jart.2025.27891.1687ENO. R.DehghanDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, IranJournal Article20240716The purpose of this document is to present the concept of bipolar fuzzy soft hypervector spaces and explore their fundamental characteristics. To begin with, a new operation and an external hyperoperation are introduced for bipolar fuzzy soft sets on the hypervector space $\mathcal{V}$, which are connected to the operation and external hyperoperation of $\mathcal{V}$. Then the notion of bipolar fuzzy soft hypervector space is defined, supported by non-trivial examples, and it is investigated whether the new bipolar fuzzy soft sets, constructed by the mentioned operation and hyperoperation, are bipolar fuzzy soft hypervector spaces. Finally, the behavior of bipolar fuzzy soft hypervector spaces under linear transformations is investigated.https://jart.guilan.ac.ir/article_8846_f12ae4a99c4cb11a5a8b047c61c04eca.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Generalized dual Leonardo quaternion numbers3748884710.22124/jart.2025.28119.1698ENF.Torunbalci AydinYildiz Technical University, Davutpasa Campus, Faculty of Chemical and Metallurgical Engineering, Department of Mathematical EngineeringJournal Article20240807In this paper, we introduce dual k-Leonardo quaternions which we call generalized dual Leonardo quaternion numbers. Some algebraic properties of these quaternions such as recurrence relation, generating function, Binet’s formula, generating function, Cassini identity, sum formulas will also be obtained.https://jart.guilan.ac.ir/article_8847_09a7553c64538ad5662b8a052e8d91b9.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Orthogonality in the category of N-complexes4957819310.22124/jart.2024.26990.1674ENE.HosseiniDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran0000-0002-0971-7548K.IzadyarDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20240531Let $\CA$ be an exact category and $\Cb_N(\CA)$ be the category of all $N$-complexes in $\CA$. If $\mathbb{X}$ is a sufficiently nice class of objects in $\Cb_N(\CA)$, then, we give a characterization of elements in the right orthogonal $\mathbb{X}^\perp$ of $\mathbb{X}$ in $\Cb_N(\CA)$ with respect to the induced exact structure.https://jart.guilan.ac.ir/article_8193_40009f809fc48bfc9091fd7210c8b32f.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401The algebraic classification of $7$-dimensional nilpotent $3$-Lie algebras5980884810.22124/jart.2025.28277.1703ENH.DarabiDepartment of Mathematics, Esfarayen University of Technology, Esfarayen, IranJournal Article20240825This paper focuses on the classification of $7$-dimensional nilpotent $3$-Lie algebras. We employ a systematic approach by considering the structure of these algebras through the central ideals. Specifically, we divide the $7$-dimensional nilpotent $3$-Lie algebra by a $1$-dimensional central ideal, resulting in a $6$- dimensional nilpotent $3$-Lie algebra. Our findings reveal the relationships between $7$-dimensional structures and their $6$-dimensional counterparts, contributing to a deeper understanding of the properties and classifications of nilpotent $3$-Lie algebras.https://jart.guilan.ac.ir/article_8848_f7ce8eeaf3ed912543ffa45fc2ccb137.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Characterization of rings by some filters8187882310.22124/jart.2025.27636.1676ENH.MouadiDepartment of Mathematics and Informatics, University Ibn Zohr, Polydisciplinary Faculty,
Lisima, Taroudant, MoroccoA.BouaDepartment of Mathematics, University Sidi Mohammed Ben Abdellah-Fez, Polydisciplinary
Faculty, Taza, MoroccoJournal Article20240605Let $R=\prod_{i\in I}R_{i}$ be the product of an infinite family of rings $\{R_{i}\}_{i\in I}$. In this study, we investigate the direct sum $\bigoplus_{i\in I}R_{i}$. Special attention is paid to the relationship between the ideal $\bigoplus_{i\in I}R_{i}$ and the $\mathcal{F}_{r}$ Frechet filter in $I$, also we show a new characterization of $\bigoplus_{i\in I}R_{i}$ by the $\mathcal{F}_{r}-\lim$.https://jart.guilan.ac.ir/article_8823_564ffe53a9facc2a3b0223a1c6549c64.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Invertibility of elements in the path algebra of a quiver8998931710.22124/jart.2025.27539.1670ENS.KarthikaDepartment of Mathematics, University of Calicut, St. Thomas College, Thrissur, IndiaM.VijiDepartment of Mathematics, University of Calicut, St. Thomas College, Thrissur, IndiaJournal Article20240524The current study elucidates the nature of right and left inverses of an element in the path algebra of a quiver. A general characterisation of such elements has been established. An explicit formula to calculate the inverse element has been formulated. It is observed that the left and right inverses of an element in the non-commutative path algebraic structure coincides. Furthermore, it is noted that the Jacobson radical of any finite dimensional path algebra can be easily found using this characterisation.https://jart.guilan.ac.ir/article_9317_55815b42d12b6f4039ab200d0e9ffd15.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401On nonnil-zero-divisor rings99114885010.22124/jart.2025.28466.1715ENS.VisweswaranDepartment of Mathematics, Saurashtra University, Rajkot, IndiaH. D.PatelScience and Humanities Department, Government Polytechnic, Bhuj, IndiaJournal Article20240915The rings considered in this paper are commutative with identity and are nonzero. Let R be a ring. An ideal I of R is said to be nonnil if I is not contained in the nilradical of R. We say that R is a nonnil-zero-divisor ring if for any proper nonnil ideal I of R, the set of zero-divisors of the R-module R/I is a finite union of prime ideals of R. This paper aims to discuss some basic properties of nonnil-zero-divisor rings and to compare the ring-theoretic properties of zero-divisor rings with that of the ring-theoretic properties of nonnil-zero-divisor rings.https://jart.guilan.ac.ir/article_8850_b4b7530b68832d57b0db7a19379fc8e2.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Join maximal element graph of lattice modules115123943110.22124/jart.2026.28291.1704ENL.SherpaDepartment of Mathematics, Savitribai Phule Pune University, Pune, IndiaV.KharatDepartment of Mathematics, Savitribai Phule Pune University, Pune, IndiaM.AgalaveDepartment of Mathematics, Fergusson College(Autonomus), Pune, IndiaN. M.PhadatareBharati Vidyapeeth Deemed to be University College of Engineering, Pune, IndiaJournal Article20240827Let $\pounds$ be a $C$-lattice and $M$ be a lattice module over $\pounds$. The join maximal element graph $\mathbb{G}(M)$ is a simple, undirected graph with all proper non-zero elements of $M$ as vertices, and two distinct vertices, $N$ and $K$, are adjacent if and only if $N\vee K\in Max(M)$, where $Max(M)$ is the collection of all maximal elements of $M$. In this paper, some properties of the graph $\mathbb{G}(M)$ like diameter, girth and clique number are investigated. Also, the interplay between the algebraic properties of $M$ and the properties of those graphs is studied.https://jart.guilan.ac.ir/article_9431_70964bf3a60bb5a4ff35d04635a81402.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Girth and planarity of the generalized Sierpi\'{n}ski gasket $S[G,t]$125137882410.22124/jart.2025.27933.1690ENF.AttarzadehDepartment of pure Mathematics, Faculty of Mathematical Sciences , University of Guilan, Rasht, IranA.AbbasiDepartment of pure Mathematics, Faculty of Mathematical Sciences , University of Guilan, Rasht, IranA.BehtoeiDepartment of Mathematics, Faculty of Science, Imam Khomeini International University,Qazvin, IranJournal Article20240714Sierpi\'{n}ski gasket graphs have many applications and are studied in diverse areas including fractal theory, topology, dynamic systems and chemistry. In this paper we study and determine the girth of generalized Sierpi\'{n}ski gasket $S[G, t]$ for an arbitrary simple graph $G$, in terms of the girth of the base graph $G$.<br />Moreover, we determine the planarity of $S[G, t]$ for some famous families of graphs.https://jart.guilan.ac.ir/article_8824_148bfb4bef2545d4aadfc3982ffa1570.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Generalized Reynolds operators and extensions of Lie-Yamaguti algebra bundle139159928710.22124/jart.2025.32090.1871ENS.GoswamiDepartment of Mathematics, Ramakrishna Mission Vivekananda Educational and Research
Institute, Howrah, India0009-0005-7864-330XG.MukherjeeAcademy of Scientific and Innovative Research (AcSIR), Ghaziabad, IndiaJournal Article20251027A Lie-Yamaguti algebra bundle is a type of algebra bundles with fibres being Lie-Yamaguti algebras, and appears naturally from geometric considerations in the work of M. Kikkawa. The aim of the present paper is to introduce the notion of generalized Reynolds operators, O-operators and Nijenhuis operators in the context of Lie-Yamaguti algebra bundle and find their applications. We also study abelian extensions of Lie-Yamaguti algebra bundles and investigate its relationship with its cohomology.https://jart.guilan.ac.ir/article_9287_3b7a8b99eaddbf23131a17a38166c1e0.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Rees ring and integral closure of a filtration161167953110.22124/jart.2026.27565.1672ENM.Yahyapour-DakhelDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranF.DorostkarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranJournal Article20240527In this paper, we will study some properties of the integral closure of a filtration relative to a module in the Rees ring.https://jart.guilan.ac.ir/article_9531_f33d860e2f91c17e4b268883f35d39e2.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Toric ideals which are determinantal169181832810.22124/jart.2025.27189.1658ENR.AbdolmalekiInstitute for Advanced Studies in Basic Sciences (IASBS), Zanjan, IranR.Zaare-NahandiInstitute for Advanced Studies in Basic Sciences (IASBS), Zanjan,IranJournal Article20240409Consider the polynomial ring $S=\mathbb{K}[x_1,\ldots, x_n]$ over a field $\mathbb{K}$. For any equigenerated monomial ideal $I \subset S$ with the defining ideal $J$ of the fiber cone $\F(I)$ generated by quadratic binomials, we introduce a matrix. The key observation is that the set of binomial $2$-minors of this matrix serves as a generating set for $J$. This framework in particular provides a characterization of the fiber cone for Freiman ideals, as well as offering a specific characterization for the fiber cone of sortable ideals.https://jart.guilan.ac.ir/article_8328_25af691b5af2bfc1b01cfd4cdddcf8bd.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Rings in which every regular ideal is projective183190882210.22124/jart.2025.27374.1662ENS. E.MahdouLaboratory of Modelling and Mathematical Structures, Faculty of Science and Technology of Fez, University S. M. Ben
Abdellah Fez, MoroccoJournal Article20240502In this paper, we introduce a new class of ring called regular hereditary ring, which is a weak version of hereditary<br />ring property. Any hereditary ring is naturally a regular hereditary ring, and in the domain context, these two forms coincide to become a Dedekind domain. We study the transfer of this notion to various context of commutative ring extensions such as localization, direct product, trivial ring extensions and pullbacks. Our results generate new families of examples of non-hereditary regular hereditary rings.https://jart.guilan.ac.ir/article_8822_c14692f698132f5935ba1eca305f8c69.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups191202885210.22124/jart.2025.28572.1719ENCh. V.VisaveDepartment of Mathematics, University of Mumbai, Mumbai, IndiaR. P.DeoreDepartment of Mathematics, University of Mumbai, Mumbai, IndiaJournal Article20240927The Power graph of a group $G$ is a graph $\mathcal{P}(G)$ with vertex set $G$ and two vertices $x$ and $y$, $x \neq y$ are adjacent if there exists some integer $k$ such that $x=y^k$ or $y=x^k$. We denote the vertex connectivity of power graph $\mathcal{P}(G)$ by $\mathcal{K}(\mathcal{P}(G))$ and the algebraic connectivity of power graph $\mathcal{P}(G)$ by $\lambda_{n-1}(\mathcal{P}(G))$. This paper investigates the upper bound for the vertex connectivity and the algebraic connectivity of $\mathcal{P}(\mathbb{Z}_{n})$. Moreover, we discuss the equivalent conditions for $\mathcal{P}(\mathbb{Z}_{n})$ to be Laplacian integral. Further the conjecture for an upper bound of the algebraic connectivity of $\mathcal{P}(\mathbb{Z}_{n})$ is posed in this article.https://jart.guilan.ac.ir/article_8852_10fb2cd4ca0718d4c59b77eab9417dd1.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401On the genus and crosscap of the total graph of commutative rings with respect to multiplication203215819010.22124/jart.2024.27463.1667ENM.NazimSchool of Computational Sciences, Faculty of Science and Technology, JSPM University, IndiaC.AbdiogluDepartment of Mathematics and Science Education, Faculty of Education, Karamano\u{g}lu Mehmetbey University, Karaman, TurkeyN.RehmanDepartment of Mathematics,
Aligarh Muslim University,
AligarhSh. A.MirDepartment of Mathematics,
Aligarh Muslim University, AligarhJournal Article20240513Let $\mathcal{S}$ be a commutative ring and $Z(\mathcal{S})$ be its zero-divisors set.<br />The total graph of $\mathcal{S}$ with respect to multiplication, denoted by $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}))$, is an undirected graph with vertex set as the ring elements $\mathcal{S}$ and two distinct vertices $\alpha$ and $\beta$ are adjacent if and only if $\alpha\beta \in Z(\mathcal{S})$.<br />The graph $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}^*))$ is a subgraph of $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}))$ with vertex set $\mathcal{S}^*$ (set of nonzero elements of $\mathcal{S}$).<br />In this paper, we characterize finite rings $\mathcal{S}$ for which $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}^*))$ belongs to some well-known families of graphs. Further, we classify the finite rings $\mathcal{S}$ for which $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}^*))$ is planar, toroidal or double toroidal. Finally, we analyze the finite rings $\mathcal{S}$ for which the graph $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}^*))$ has crosscap at most two.https://jart.guilan.ac.ir/article_8190_c98ff57cf45563db038093829ef851ed.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401On the bicomplex Fibonacci $p$ quaternions217233952410.22124/jart.2026.27743.1682ENB.PrasadDepartment of Mathematics, Kandi Raj College, Kandi, IndiaJournal Article20240620The paper introduces a novel bicomplex Fibonacci p quaternions, establishing algebraic properties, Honsberger identity, D’Ocagne’s identity, Cassini’s identity, Catalan’s identity for these quaternions. The study extends previous work on bicomplex Fibonacci quaternions [10] by incorporating bicomplex Fibonacci p quaternions. These new quaternions may have implications in applied mathematics, quantum mechanics, quantum physics, Lie groups, Kinematics and differential equations.https://jart.guilan.ac.ir/article_9524_8c862dcdc4b28bac6fc6065a1c683387.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401On Closedness of Subvarieties of Bands235245952610.22124/jart.2026.27992.1692ENSh.AbbasDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaW.AshrafDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaA.PrakashDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaJournal Article20240722In this paper, first we proved that all subvarieties of the variety of left (right) regular bands are closed in the variety of $n$-nilpotent extension of bands. Secondly, we proved the closedness of rectangular bands in the variety $\mathcal{V}=[ac=ab^nc]$ $(n\in \bf N)$, of semigroups. Further, we have shown that all subvarieties of the variety of left (right) normal bands are closed in the variety $\mathcal{V}=[axy=a^py^qx^r]$ $(p,q,r\in \bf N)$, of semigroups and lastly, we proved that all subvarieties of the variety of left (right) quasinormal bands are closed in the variety $\mathcal{V}=[axy=a^px^qa^ry]$ $(p,q,r\in \bf N)$, of semigroups.https://jart.guilan.ac.ir/article_9526_9ad7dca10cbf269e3feeff1de29fb84a.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401On the unitary Cayley graphs of group rings247255952510.22124/jart.2026.28297.1705ENK.LimkulDepartment of Applied Mathematics and Statistics, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun, ThailandS.NantaDepartment of Applied Mathematics and Statistics, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun, ThailandJournal Article20240901Let $R$ be a ring. The unitary Cayley graph of a ring $R$, denoted by $\Gamma(R)$, is a graph with vertex set $R$ where two vertices $u,v\in R$ are adjacent if and only if $u-v$ is a unit of $R$. In this paper, we investigate the unitary Cayley graph of a finite ring, called a group ring, and examine its fundamental properties. We present the conditions for adjacency, the connectivity of the graph and its basic structure. Additionally, we provide the exact value of the degree of a vertex and the distance between any two vertices within the graph.https://jart.guilan.ac.ir/article_9525_9b5c4422dd7362b6f2fb357bc67f160b.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).20260401Identification Gorenstein rings via special semidualizing modules257265885110.22124/jart.2025.28567.1720ENM.BagheriDepartment of Mathematics,
Imam Khomeini International University, Qazvin, IranA. J.TaherizadehFaculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, IranR.VesalianFaculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, IranJournal Article20240930Let $(R, {\frak m})$ be a Noetherian local ring and $M$ be a finitely generated $R$-module such that ${\rm Hom}_R(M,R) \cong \underset{i=1}{\overset{n}{\oplus}} C$ for some positive integer $n$. We try to present new characterizations of Gorenstein rings via $M$ and $C$. It is proved that if ${\rm depth}\, R=0$ and ${\rm id}_R (M) < \infty$ then $R$ is Gorenstein. Also, it is shown that if $M$ is a Cohen-Macaulay $R$-module with finite injective dimension, then $R$ is Gorenstein.https://jart.guilan.ac.ir/article_8851_bddae1840579fd5475d0cdb4194d35ef.pdf