University of GuilanJournal of Algebra and Related Topics2345-393113120250701New models of four dimensional absolute valued algebras114818610.22124/jart.2024.25857.1592ENN.MotyaDepartment of Mathematics, Sidi Mohamed Ben Abdellah University, Faculty of Scinces
Dhar El Mahraz, Fez-Atlas, MoroccoM.HakimaDepartment of Mathematics, Sidi Mohamed Ben Abdellah University, Faculty of Scinces
Dhar El Mahraz, Fez-Atlas, MoroccoA.MoutassimRegional Center For Education And Training Professions, Casablanca-Settat, MoroccoJournal Article20231023This paper deals with some results concerning the 4-dimensional absolute valued algebras with left omnipresent unit. We also construct, by algebraic methods some new models of 4-dimensional absolute valued algebras with left omnipresent unit. These new algebras contain at least one 2-dimensional sub-algebra, and aren't isomorphic to $\mathbb{H}$ ( The quaternion algebra).https://jart.guilan.ac.ir/article_8186_46724854f8b6e668cb6bebf03e393870.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Hesitant hybrid interior ideals in semigroups1529818510.22124/jart.2024.25776.1589ENM.DeepikaDepartment of Mathematics, Karunya Institute of Technology and Sciences, Tamilnadu, IndiaB.ElavarasanDepartment of Mathematics, Karunya Institute of Technology and Sciences, Tamilnadu, IndiaJ.Catherine Grace JohnDepartment of Mathematics, Karunya Institute of Technology and Sciences, Tamilnadu, India0000-0002-3352-3436Journal Article20231016Hesitant fuzzy sets are very useful for dealing with group decision-making problems when experts have hesitation among several possible memberships for an element in a set. Recently, many researchers have used these concepts in clustering analysis and decision-making. In this article, the notions of hesitant hybrid subsemigroups and hesitant hybrid left<br />(resp., right) ideals in a semigroup are introduced, and several properties are investigated. The concept of hesitant hybrid product is also introduced, and properties of hesitant hybrid subsemigroups and hybrid left (resp., right) ideals are considered using the notion of hesitant hybrid product. Relations between hesitant hybrid intersection and hesitant hybrid product are exhibited. Additionally, we establish hesitant hybrid interior ideals in semigroups and study their<br />properties. Furthermore, we prove that in regular and intra-regular semigroups, the hesitant hybrid ideal and the hesitant hybrid interior ideals are coincide.https://jart.guilan.ac.ir/article_8185_a0478fbb00a74a90b1e3856628088559.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701$\mathcal{LA}$-semiperfect modules3137843610.22124/jart.2024.24830.1544ENB. N.TürkmenDepartment of Mathematics, Faculty of Art and Science, Amasya university, İpekköy Amasya, TurkeyJournal Article20230627Inspired in [7], we strengthened semiperfect modules to $\mathcal{LA}$-semiperfect modules by adding the concept of locally artinian submodule and we proved that the concept of these modules is not empty. Then we characterized these projective modules with the help of defining $\mathcal{LA}$-projective covers. Thus we achived the necessary and sufficient condition for the projective module between the notion of $\mathcal{LA}$-semiperfect modules and the notion of locally artinian supplemented modules.https://jart.guilan.ac.ir/article_8436_5e571590197ade80339b0ae4aed12319.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Multipliers on certain topological algebras3944843310.22124/jart.2024.24814.1543ENM.Shams YousefiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranJournal Article20230625There are many well-known results on multipliers (particularly multipliers with closed range) defined on a commutative semisimple Banach algebra. After stating some of them, similar results will be given for commutative strongly semisimple normed algebras and commutative (not necessarily semisimple) Banach algebras.https://jart.guilan.ac.ir/article_8433_c66b01d413c6634979c71d3f994bd98c.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701The co-prime power order graph of a finite group4552843810.22124/jart.2024.24886.1547ENH. H.MushatetMinistry of Education, Dhi Qar Education Directorate, IraqA. A.TalebiDepartment of Mathematics, University of Mazandaran, Babolsar, IranJournal Article20230703In this study, we generalized the co-prime graph of a finite group called the co-prime power order graph of a finite group. It is denoted by $\beta_G$, and its vertex set is $G$, such that two distinct vertices $x$ and $y$ are adjacent if and only if $\operatorname{gcd}(|x|,|y|)=p^n$, where $p$ is a prime number, and $n \in \mathbb{Z}^{+} \cup\{0\}$. We characterized complete graphs and planar graphs on the co-prime power order graphs, and investigated some properties of graph $\beta_G$ for some groups such as cyclic groups, dihedral groups, and the generalized quaternion groups, and obtained the vertex-connectivity among them. Finally, we characterized some induced subgraphs of co-prime power order graph for some finite groups.https://jart.guilan.ac.ir/article_8438_4e58225938ad28bad8d3a074b8205947.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Classification of 3-GNDB graphs5360843410.22124/jart.2025.25226.1569ENS. A.HosseiniDepartment of Mathematics, Islamic Azad University, Nazarabad Branch, Nazarabad, IranM.AlaeiyanDepartment of Mathematics, Iran University of Science and Technology, Narmak, Tehran, IranZ.AliannejadiDepartment of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran0000-0001-6133-1047Journal Article20230810A nonempty graph $\Gamma$ is called generalized 3-distance-balanced, (3-$GDB$) whenever for every edge $ab$, $|W_{ab}|=3|W_{ba}|$ or conversely. As well as a graph $\Gamma$ is called generalized 3-nicely distance-balanced (3-$GNDB$) whenever for every edge $ab$ of $\Gamma$, there exists a positive integer $\gamma_\Gamma$, such that: $|W_{ba}|=\gamma_\Gamma$.In this paper, we classify 3-$GNDB$ graphs with, $\gamma_\Gamma\in \{1,2\}$.https://jart.guilan.ac.ir/article_8434_592d293cea0892a20cac722eda68cf28.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Dedekind N-group and uniform N-group in near-rings6172882010.22124/jart.2025.24773.1541ENT.RoodbarylorDepartment of mathematics, Kerman Branch, Islamic Azad University, Kerman, IranM.SadeghiDepartment of Mathematics, University of Nobonyad, Sirjan, IranJournal Article20230618In this paper the authors have defined Dedekind $N$-groups, prime $N$-groups, uniform $N$-groups in near rings and have found the relationship between them. For example they have showed the notions uniform $N$-group and Dedekind $N$-group in near rings are equivalent.https://jart.guilan.ac.ir/article_8820_1d8a11ca3fda2fee9bbfa70f1a25cf72.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701On the solutions of the Diophantine equation $F_{n_1}+F_{n_2}+F_{n_3}+F_{n_4}=11^a$7385843510.22124/jart.2024.24741.1540ENB.Earp-LynchDepartment of Mathematics, Carleton University, Ottawa, CanadaS.Earp-LynchDepartment of Mathematics, Carleton University, Ottawa, CanadaA.El BazDepartment of Mathematics, La Facult\'e des Sciences Dhar El Mahraz F\`{e}s, F\`es, MoroccoJournal Article20230616Let $F_{n}$ denote the $n$th Fibonacci number. In this paper, we solve the Diophantine equation $F_{n_1}+F_{n_2}+F_{n_3}+F_{n_4}=y^a$ in integers $n_1,n_2,n_3,n_4,a$ for $y=11$. In doing so, we disprove a recent conjecture made by Diouf and Tiebekabe in \cite{D-T}.https://jart.guilan.ac.ir/article_8435_1d9652d1efc6714f48ad6a7a7d7e9d14.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701A note on total graph of commutative krasner hyperrings8797844010.22124/jart.2024.24911.1553ENE.NavidiniaDepartment of Mathematics, University of Mohaghegh Ardabili, Ardabil, IranA.KhojaliDepartment of Mathematics, University of Mohaghegh Ardabili, Ardabil, IranF.Esmaeili Khalil SaraeiFouman Faculty of Engineering, College of Engineering, University of Tehran, Fouman, IranJournal Article20230712The purpose of this paper is to introduce the notion of total graph of Krasner hyperrings. In this regard, a connection between the graph theory and the theory of hyperrings is constructed and some fundamental properties of the total graph of Krasner hyperrings are investigated. Finally, for a multiplicative-prime subset $H$ of a hyperring $R$, the diameter and the girth of $\Gamma_{\!\!H}(R\setminus H)\,\mbox{and}\, \Gamma_{\!\!H}(H)$ are computed precisely.https://jart.guilan.ac.ir/article_8440_c61114a62165a04f2aab15fbfafc8c99.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Some additive results for the g-Drazin inverse of operators99107882110.22124/jart.2025.25909.1595ENM.SheibaniFarzanegan Campus, Semnan University, Semnan, IranF.TayebiDepartment of Mathematics, Statistics and Computer Science, Semnan University, Semnan,
IranN.AshrafiDepartment of Mathematics, Statistics and Computer Science, Semnan University, Semnan,
IranR.BahmaniDepartment of Mathematics, Statistics and Computer Science, Semnan University, Semnan,
IranJournal Article20231031The motivation of this article, is to establish new additive results for the g-Drazin inverse of linear operators over Banach spaces. Following the applicability of the g-Drazin inverse of operator matrices in solving the systems of linear differential equations, we then apply our results to operator matrices and obtain some results on generalized Drazin inverse of block<br />operator matrices.https://jart.guilan.ac.ir/article_8821_6c3241ca8efc93feb12dd4cdcfa9f97a.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701On primal topological groups109116818710.22124/jart.2024.25894.1593ENA.MuneeshkumarDepartment of Mathematics, PSR Arts and Science College, Sivakasi, TamilnaduP.GnanachandraCentre for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal
College, Sivakasi, TamilnaduS.JafariDepartment of Mathematics, College of Vestsjaelland South, 4200 Slagelse, DenmarkJournal Article20231028In this paper, we introduce the notion of primal topological group, which is a generalization of topological group by a primal. We discuss the characterizations of primal topological groups with illustrative examples.https://jart.guilan.ac.ir/article_8187_1ba7a064e5319a6d825e59f77f400576.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Weak cotorsion modules with respect to an integer and a semidualizing bimodule117134820510.22124/jart.2024.26049.1604ENM.AminiDepartment of Mathematics, University of Payame Noor, Tehran, IranA.VahidiDepartment of Mathematics, University of Payame Noor, Tehran, IranE.ChamaniDepartment of Mathematics, University of Payame Noor, Tehran, IranJournal Article20231117Let $R$ and $S$ be rings, $C= {}_SC_R$ a faithfully semidualizing bimodule, and $m$ a non-negative integer. In this paper, we present some homological properties relative to the class of $R$-modules of $C$-weak injective dimension at most $m$ and the class of $S$-modules of $C$-weak flat dimension at most $m$. We introduce and study weak cotorsion modules with respect to $m$ and $C$ by using the class of modules of $C$-weak flat dimension at most $m$.https://jart.guilan.ac.ir/article_8205_c1a5f37953ac2bbb7910e57e9371cb0f.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Ordered maps and kernels of OBCI-algebras135157843910.22124/jart.2024.24864.1546ENE.YangDepartment of Philosophy, Institute of Critical Thinking and Writing, Jeonbuk National
University, Jeonju, KoreaE. H.RohDepartment of Mathematics Education, Chinju National University of Education, Jinju,
KoreaY. B.JunDepartment of Mathematics Education, Gyeongsang National University, Jinju, KoreaJournal Article20230701Yang-Roh-Jun recently introduced the notion of ordered BCI-algebras as a generalization of BCI-algebras. They further introduced the notions of homomorphisms of ordered BCI-algebras and studied associated properties. Here we generalize homomorphisms into ordered maps, i.e., order-preserving maps. More precisely, the notions of ordered maps and kernels of ordered BCI-algebras are first defined. Next, properties related to (ordered) subalgebras, (ordered) filters and direct products of ordered BCI-algebras are addressed.https://jart.guilan.ac.ir/article_8439_ad11a956ab42beeea82573392e6ada43.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Strongly weak idempotent nil -clean rings159172818410.22124/jart.2024.25294.1570ENB.AsmareDepartment of Mathematics, College of Natural and Computational Science, Addis Ababa University, Addis Ababa, EthiopiaT.AbebawDepartment of Mathematics, College of Natural and Computational Science, Addis Ababa University, Addis Ababa, EthiopiaK.VenkateswarluDepartment of Computer Science and Systems Engineering, College of Engineering, Andhra University, Visakhapatnam, Andhra Pradesh, IndiaJournal Article20230817We introduce the concept of strongly weak idempotent nil-clean rings which is a generalization of strongly weakly nil clean rings. We characterize strongly weak idempotent nil-clean rings in terms of the set of nilpotent elements, homomorphic images, and Jacobson radicals. We prove that a ring $R$ is strongly weak idempotent nil-clean if and only if for any $a\in R$, $a-a^3$ is nilpotent if and only if $Nil(R)$ forms an ideal and $R/{Nil(R)}$ is reduced weak idempotent nil-clean if and only if $R$ has no homomorphic image $\mathbb{Z}_3\oplus \mathbb{Z}_3$ and $a^2-a^4$ is nilpotent. Moreover, we prove that a strongly weak idempotent nil-clean ring $R$ with $2\in J(R)$ satisfies nil-involution property.https://jart.guilan.ac.ir/article_8184_5c5d34200ea3a4d215aea9ba6b7ad531.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393113120250701Weak u-s-projective modules and dimensions173188843710.22124/jart.2024.24832.1545ENR. A.AssaadDepartment of Artificial Intelligence, Faculty of Computer Science & Information Technology, Al-Razi University, Sana'a, YemenX.ZhangSchool of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, ChinaJournal Article20230628The primary focus of this paper is to introduce and investigate a fresh category of projective modules, referred to as weak $u$-$S$-projective modules ($w$-$u$-w-u- is an abbreviation for weak uniformly). These novel modules are utilized for characterizing $u$-$S$-von Neumann regular rings. Additionally, the paper investigates a new type of rings, named $u$-$S$-semihereditary rings. This leads to the introduction of the weak $u$-$S$-projective dimensions of modules and weak $u$-$S$-global dimension of rings in this paper.https://jart.guilan.ac.ir/article_8437_48f724dbc2f9b8f002803addf4a48d15.pdf