University of GuilanJournal of Algebra and Related Topics2345-393113220251201Ordered BCI-algebras, Y-kernels and (ordered) functions113819810.22124/jart.2024.26608.1626ENE.YangDepartment of Philosophy, Jeonbuk National University, Jeonju 54896, KoreaE. H.RohDepartment of Mathematics Education,
Chinju National University of Education, Jinju 52673, KoreaY. B.JunDepartment of Mathematics Education
Gyeongsang National University
Jinju 52828, KoreaJournal Article20240127The concept of kernels in ordered BCI-algebras was first introduced by Yang-Roh-Jun. This paper extends the concept to specific kernels, called here Y-kernels. To be more precise, two sorts of Y-kernels related to function were first introduced and the relations between them and between these Y-kernels and kernels were studied. Next, related to ordered function (and (ordered) homomorphism) the same relations are investigated.https://jart.guilan.ac.ir/article_8198_915310a52be862b9f2d0b33090364389.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201An extension of commutativity degree of finite groups1526820110.22124/jart.2024.26440.1616ENM.HashemiFaculty of Mathematical Sciences, University of Guilan, Rasht, IranS.GorjianDepartment of Mathematics, University Campus 2, University of Guilan, Rasht, IranJournal Article20240110Let G be a finite group. The commutativity degree of G, written d(G), is defined as the ratio<br />|{(x, y)|x, y \in G, xy = yx}|/|G|^2. In this paper, we first extend this concept of finite groups to the<br />commutativity degree of fuzzy subgroups. Then, by using the numerical solutions of the equation xy − zu \eqiv t(mod n), we give explicit formulas for the commutativity degree of fuzzy subgroups of 2-generated groups of nilpotency class 2. Finally we show that this method also works for a large class of finite groups, including<br />metabelian groups.https://jart.guilan.ac.ir/article_8201_d9a5688aad7d483158b1f5a5b63253a2.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201On $\mathbb{Z}_k-$vertex-magic labeling of prime graph $PG(\mathbb{Z}_n)$2737818810.22124/jart.2024.26022.1601ENM. H.KhuluqDepartment of Mathematics, Faculty of Mathematics and Sciences, University of Brawijaya, Malang, IndonesiaV. H.KrisnawatiDepartment of Mathematics, Faculty of Mathematics and Sciences, University of Brawijaya, Malang, IndonesiaN.HidayatDepartment of Mathematics, Faculty of Mathematics and Sciences, University of Brawijaya, Malang, IndonesiaJournal Article20231114Let $G=(V(G),E(G))$ be a graph, $(\mathcal{A},+)$ be an Abelian group with identity $0_{\mathcal{A}}$, and $(\mathcal{{R}},+,\cdot)$ be a ring. The $\mathcal{A}$-vertex-magic labeling of $G$ is a mapping from $V(G)$ to $\mathcal{A}-\{0_{\mathcal{A}}\}$ such that the total labels of every adjacent vertex with $u$ are equal for every $u$ in $V(G)$. The prime graph over ${\mathcal{R}}$, denoted by $PG(\mathcal{R})$, is a graph with $V(PG(\mathcal{R}))={\mathcal{R}}$ such that $uv$ is an edge if and only if $u\mathcal{R}v=\{0_{\mathcal{R}}\}$ or $v{\mathcal{R}}u=\{0_{\mathcal{R}}\}$, for every vertex $u\neq v$. In this article, we discuss the $\mathbb{Z}_k$-vertex-magic labeling of the prime graph over ther ring $\mathbb{Z}_n$. We study some literature to develop the properties of $\mathbb{Z}_k$-vertex-magic labeling of $PG(\mathcal{R})$. We investigate some classes of prime graphs over ring $\mathbb{Z}_n$ for $n=p, n=p^2,$ and $n=pq$, with $p\neq q$ primes.https://jart.guilan.ac.ir/article_8188_25884885eb3ff8ae2285ffda281a2628.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201A note on dimension of local cohomology modules3942820310.22124/jart.2024.26183.1609ENM.AmanalahzadehUniversity of Mohaghegh ArdabiliJ.AzamiDeprtment of Mathematics, Faculty of Sciences, University of Mohaghegh ArdabiliM.ShafieiPayame noor UniversityI.BagheriyehIslamic Azad UniversityJournal Article20231201Let $(R, m)$ be a commutative Noetherian local ring and $I$ be an ideal of $R$. In this paper first we find new results about the dimension of the local cohomology module $H^i_I(R)$. Then we will obtain new relations between the invariants such as arithmetic rank, cohomological dimension, krull dimension, and the height of an ideal of $R$.https://jart.guilan.ac.ir/article_8203_647ea211637407fda4131062625ed1be.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Berwald and Douglas spaces of a Finsler space with deformed Berwald-Infinite series metric4352820010.22124/jart.2024.26510.1622ENB. K.TripathiScience and Humanities Department, Faculty of Mathematics, L D. College of Engineering AhmedabadS.PrajapatiScience Mathematics Branch, Gujarat Technological University, Chandkheda, Ahmedabad-382424Journal Article20240118In the present paper, we have studied the basic properties of the Berwald and Douglas spaces of a Finsler space with the deformed Berwald-Infinite series metric and examined the condition under which the Finsler space with deformed Berwald-Infinite series metric will be a Berwald and Douglas space.https://jart.guilan.ac.ir/article_8200_1bea7e17c1a6a9b135608ee9de78410d.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Lie-Yamaguti algebra bundle5373927010.22124/jart.2025.26889.1638ENS.GoswamiDepartment of Mathematics, Ramakrishna Mission Vivekananda Educational and Research Institute, Howrah, India0009-0005-7864-330XG.MukherjeeAcademy of Scientific and Innovative Research (AcSIR), Ghaziabad, IndiaJournal Article20240229We introduce the notion of Lie-Yamaguti algebra bundle, and show that such bundles appeared naturally from geometric considerations in the work of M. Kikkawa. This motivates us to introduce this object in the proper mathematical framework. We define cohomology groups of such bundles with coefficients in a representation extending the definition of cohomology groups of Lie-Yamaguti algebras.https://jart.guilan.ac.ir/article_9270_4146f1fe1c5cde938e424c4d7b70ca32.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201A Zariski-like topology on the 2-prime spectrum of commutative rings7584819610.22124/jart.2024.26914.1640ENH.Roshan ShekalgourabiDepartment of Basic Sciences, Arak University of Technology, Arak, IranD.Hassanzadeh LelekaamiDepartment of Basic Sciences, Arak University of Technology, Arak, IranJournal Article20240303A proper ideal $P$ of a ring $R$ is called \emph{2-prime} if for all $x, y \in R$ such that $xy\in P$, then either $x^2 \in P$ or $y^2 \in P$. In this paper, we introduce a Zariski topology on the set of all 2-prime ideals of commutative rings. We investigate this topology and clarify the interplay between the properties of this topological space and the algebraic properties of the ring under consideration.https://jart.guilan.ac.ir/article_8196_7089e094eeb208c8aa66958498b0ca7e.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Some properties of FP-injective modules over group rings8598819210.22124/jart.2024.27046.1651ENA.HajizamaniDepartment of Mathematics, University of Hormozgan, Bandarabbas, Iran.Journal Article20240316FP-injective modules, which are also called absolutely pure modules, play an important role in characterizing some classical rings such as semihereditary, Noetherian, von-Neumann regular, and coherent rings. These modules have excellent properties over coherent rings similar to injective modules over Noetherian rings. In the present article, we study this class of modules over the group ring $\rga$ of a group $\ga$, concerning a commutative ring $R$. We show that if $\gb$ is a finite index subgroup of $\ga$, then the restriction of scalars along the natural ring homomorphism $\rgb\rightarrow \rga$ and its right adjoint $\rga\otimes_{\rgb}-$ preserve FP-injective modules. We will also examine the properties of FP-injective modules over the group ring of $\LHF$-groups. Next, we will switch to the so-called Ding-Chen rings. These rings are coherent versions of Iwanaga-Gorenstein rings, where Noetherian and self-injectivity are replaced by coherence and self-FP-injectivity, respectively. In particular, we have investigated the ascent and descent of the Ding-Chen property between the rings $\rga$ and $\rgb$.https://jart.guilan.ac.ir/article_8192_3bfa163a073a7dca7f16e0d9cf134e72.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Remarks on the zero-set intersection graph99108927110.22124/jart.2025.27038.1652ENP.DharDepartment of Mathematics, North-Eastern Hill University, Shillong, IndiaJ. P. J.KharbhihDepartment of Mathematics, North-Eastern Hill University, Shillong, IndiaJournal Article20240317In this paper, we study the zero-set intersection graph ($\Gamma(C(X))$) and its line graph ($L(\Gamma(C(X)))$). We showed that $0$ is a cut vertex of $\Gamma(C(X))$ iff $|X|=2$, and for a first countable space $X$, $\Gamma(C(X))$ is chordal iff $|X|=2 \ or\ |X|=3.$ We stated some conditions for a maximal clique to be a maximal ideal. We obtained that two (first countable/real compact) topological spaces $X$ and $Y$ are homeomorphic iff $L(\Gamma(C(X)))$ is graph isomorphic to $L(\Gamma(C(Y)))$ iff $C(X)$ is isomorphic to $C(Y).$ We showed that $\{f,g\}$ is a dominating set of $\Gamma(C(X))$ iff $fg=0.$https://jart.guilan.ac.ir/article_9271_1701cbcecd972aee118e3b66e34fc608.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201On non-closure degree for finite groups109117927210.22124/jart.2025.26910.1639ENA.SuleimanDepartment of Mathematics, Air Force Institute of Technology, Kaduna, NigeriaN. M.Mohd AliDepartment of Mathematical Sciences, Universiti Teknologi Malaysia, Johor, MalaysiaA. I.KiriDepartment of Mathematical Sciences, Bayero University, Kano, NigeriaJournal Article20240303The non-closure degree for a finite group $G$ has to do with obtaining a probability of selecting any pair of elements $x, y \in G$ such that $xy \notin H$, where $H$ is normal in $G$. It is shown in the paper that the probability lies in the interval $[ 0 , \frac{|G| - 1}{|G|}$ ), with the result as 0 if and only if $H=G$. Illustrations were done using both abelian and non-abelian groups relative to their normal subgroups.https://jart.guilan.ac.ir/article_9272_07486103c3772630573499fbb04b4c49.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Another view of BZ-algebras119135820210.22124/jart.2024.26251.1612ENT.OnerDepartment of Mathematics, Faculty of Science, Ege University, Izmir, TurkeyT.KaticanDepartment of Mathematics, Izmir University of Economics, Izmir, TurkeyA.Borumand SaeidDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar
University of Kerman, Kerman, IranJournal Article20231212In this work, Sheffer stroke BZ-algebra (briefly, SBZ-algebra) is introduced and its properties are examined. Then a partial order is defined on SBZ-algebras. It is shown that a Cartesian product of two SBZ-algebras is an SBZ-algebra. After giving SBZ-ideals and SBZsubalgebras, it is proved that any SBZ-ideal of an SBZ-algebra is an ideal of this SBZ-algebra and<br />vice versa, and that it is also an SBZ-subalgebra. Also, a congruence relation on an SBZ-algebra is determined by an SBZ-ideal, and the quotient of an SBZ-algebra by a congruence relation on this algebra is constructed. Thus, it is proved that the quotient of the SBZ-algebra is an SBZalgebra. Furthermore, we define SBZ-homomorphisms between SBZ-algebras and state that the kernel of an SBZ-homomorphism is an SBZ-ideal and so an SBZ-subalgebra. Hence, a new SBZ-homomorphism is described by means of the kernel of an SBZ-homomorphism. Finally, we show that some properties are preserved under SBZ-homomorphisms.https://jart.guilan.ac.ir/article_8202_5d114a06b537f29eb543b066eebc222a.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Extensions of soft fractional Ideals using soft semistar operations approach on Integral domains137148819510.22124/jart.2024.26958.1644ENT. R.MirDepartment of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi, IndiaM. Y.AbbasiDepartment of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi, IndiaJournal Article20240306A comprehensive mathematical technique for handling uncertainty is the Molodtsov introduced idea of soft sets. In this paper, the operations leading to themselves from the set of undeniable soft fractional ideals are instigated. We provide some extensions of soft fractional ideals using the notion of overrings. We bring out the notion of soft semistar operations in relation to undeniable soft fractional ideals and connect it to the current notions of star and semistar operations. We also demonstrate the formation of complete soft lattice from the collection of all soft semistar operations on integral domains.https://jart.guilan.ac.ir/article_8195_05b92f33df70b28d313de73580289223.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201A class of number fields without odd rational prime index divisors149163819110.22124/jart.2024.27125.1656ENJ.DidiDepartment of Mathematics, LSI Laboratory, University of Sidi Mohamed Ben Abdellah,
Route d’Oujda, Taza, MoroccoM.SahmoudiDepartment of Mathematics, University of Moulay Ismail, Zitoune, Meknes, MoroccoA.ChillaliDepartment of Mathematics, LSI Laboratory, University of Sidi Mohamed Ben Abdellah,
Route d’Oujda, Taza, MoroccoJournal Article20240330In this work, for every number field $K$ generated by a root of a monic irreducible trinomial $F(x) = x^{7} + a.x^{6} + b \in \mathbb{Z}[x]$, we show that no odd rational prime $p$ divides the index $i(K)$, and we give the necessary and sufficient conditions on a, b such that $2$ divides $i(K)$. Specifically, we provide adequate requirements for $K$ to be non-monogenic. Finally, several computational examples are used to illustrate our conclusions.https://jart.guilan.ac.ir/article_8191_caa44b91225ddeb8b9d632a9e5b5adbd.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Commutativity of prime rings involving multiplicative b-generalized derivation165176843210.22124/jart.2025.26837.1635ENW.AhmedDepartment of Mathematics, Sreenidhi University, Hyderabad, IndiaM. R.MozumderDepartment of Mathematics,
Aligarh Muslim University, Aligarh, IndiaA.AbbasiSchool of Advanced Science and Languages, VIT Bhopal University, Madhya Pradesh, IndiaH. M.AlnoghashiDepartment of Mathematics, Amran University, Amran, YemenJournal Article20240223Let $\Qa_{mr}$ be a maximal right ring of quotients of $\Aa$, where $\Aa$ is a prime ring. A map $\Fa : \Aa \rightarrow \Qa_{mr}$ associated with derivation $d : \Aa \rightarrow \Aa$ is called a multiplicative $b$-generalized derivation (need not necessarily additive) if $\Fa(l m ) = \Fa(l )m + bl d(m )$ holds for all $l ,m \in \Aa$ and for some $b \in \Qa_{mr}$. In this article, we study the commutativity of prime rings when the map $b$-generalized derivation satisfies the strong commutativity preserving condition and some central identities.https://jart.guilan.ac.ir/article_8432_bb7989e7ca919763886b5aa3d3515c5b.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201The domination uniform subdivision number of $G^{++-}$177185819910.22124/jart.2024.26561.1624ENT. B.MagizhaSt. Xaviers Catholic College of Engineering (Autonomous), NagercoilA.JebithaDepartment of Mathematics, Holy Cross College (Autonomous), NagercoilS.SujithaDepartment of Mathematics, Holy Cross College (Autonomous) Nagercoil, Tamilnadu, IndiaJournal Article20240123Theory of domination plays a vital role in network communications. Different domination parameters have been studied by various mathematicians. In this paper, the exact value of domination uniform subdivision number of transformation graphs $G^{++-}$ of some standard graphs are obtained. Furthermore, the bounds of ${usd}_\gamma (G^{++-})$ for any graph $G$ are obtained. Finally, ${sd}_ \gamma - $critical graph on $G^{++-}$ are characterized.https://jart.guilan.ac.ir/article_8199_ee37a89f23fa72918d18b22b0b811c05.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Some results on $2$-absorbing $ R_{\Gamma}-$semimodules over $ \Gamma-$semirings187198819710.22124/jart.2024.26633.1627ENH. K.RanoteDepartment of Mathematics, Maharaja Agarsen University, (Baddi) Solan, IndiaJournal Article20240130The purpose of this paper is to introduce the notion of 2-absorbing $ R_{\Gamma}-$semimodules over $ \Gamma-$semirings, as a generalization of 2-absorbing semimodules over semirings and study various results related to them.https://jart.guilan.ac.ir/article_8197_c54e1ef28aef78bc5c27d25f6defc288.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113220251201Stability of the depth function of good filtrations199208927310.22124/jart.2025.27064.1654END. F. J.KouakouLaboratoire de Mathématiques et Informatique, Université Nangui Abrogoua, UFR - SFA, Côte d'IvoireA.AssaneLaboratoire de Mathématiques et Informatique, Université Nangui Abrogoua, UFR - SFA, Côte d'IvoireD.KamanoDepartement de Sciences et Technologie, Ecole Normale Supérieure d'Abidjan, Côte d'IvoireJournal Article20240321Let $A$ be a Noetherian local ring, and let $I \subset J$ be two ideals of $A$. Let $M$ be a finitely generated $A$-module. Brodmann proved that the function $n \mapsto \mathrm{depth}_{J}(\frac{M}{I^{n}M})$ is constant for large $n$.<br />In this paper, we consider a filtration $\phi = (M_n)_{n \in \mathbb{N}}$ of $M$ and a filtration $f = (I_n)_{n \in \mathbb{N}}$ of $A$. Generalizing Brodmann's result, we first show that the function $n \mapsto \mathrm{depth}_{J}(\frac{M}{M_{n}})$ is constant for large $n$ of value $\mathrm{depth}_{J}(f, M)$, provided that $\phi$ is $f$-good and $f$ is strongly Noetherian. Secondly, we establish the inequality $\gamma_{J}(f, M) \leq \dim_A(M) - \mathrm{depth}_{J}(f, M)$, where $\gamma_{J}(f, M)$ denotes the analytic spread of $f$ at $J$ with respect to $M$. https://jart.guilan.ac.ir/article_9273_8693396ffa0f72a744d2867a5cf3e292.pdf