University of GuilanJournal of Algebra and Related Topics2345-393111120230601\L{}ukasiewicz fuzzy ideals in BCK-algebras and BCI-algebras114630710.22124/jart.2022.21963.1393ENY. B.JunDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea0000-0002-0181-8969Journal Article20220316The notion of (closed) \L{}ukasiewicz fuzzy ideal is introduced, and several properties are investigated.<br />The relationship between \L{}ukasiewicz fuzzy subalgebra and \L{}ukasiewicz<br />fuzzy ideal is discussed, and characterization of a \L{}ukasiewicz fuzzy ideal is considered.<br />Conditions for a \L{}ukasiewicz fuzzy subalgebra to be a \L{}ukasiewicz fuzzy ideal are provided, and<br />conditions for the $\in$-set, $q$-set and $O$-set to be ideals are explored.https://jart.guilan.ac.ir/article_6307_6c44c56d6fd38fa7b8a59896d1800b2c.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601Some properties of pair of n-isoclinism induction1526624610.22124/jart.2022.20858.1330ENM.SajediDepartment of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, IranH.DarabiDepartment of Mathematics, Esfarayen University of Technology, Esfarayen, IranJournal Article20211018Let $(G,M)$ be a pair of groups, in which $M$ is a normal subgroup of a group $G.$ We study some properties of $n$-isoclinism of pair of groups. In fact, we show that the subgroups and quotient groups of two $n$-isoclinism pair of groups are $m$-isoclinic for all $m\le n.$ Moreover, the properties of $\pi$-pair and supersolvable pair of groups which are invariant under $n$-isoclinism has be studied.https://jart.guilan.ac.ir/article_6246_71d0d7ed09fe7e40aa63d80e51160bca.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601On Almost $S$-prime submodules2742676910.22124/jart.2022.22862.1427ENF.FarzalipourDepartment of Mathematics, Payame Noor University, Tehran,
Iran.R.GhaseminejadDepartment of Mathematics, Payame Noor University, Tehran, IranM. S.SayedsadeghiDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20220830Let $R$ be a commutative ring with non-zero identity, $S\subseteq R$ be a multiplicatively closed subset of $R$ and let $M$ be an $R$-module. A submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ is said to be almost $S$-prime, if there exists an $s\in S$ such that whenever $rm\in N-(N:_{R}M)N$, then $sm\in N$ or $sr\in (N:_{R}M)$ for each $r\in R$, $m\in M$. The aim of this paper is to introduce and investigate some properties of the notion of almost $S$-prime submodules, especially in multiplication modules. Moreover, we investigate the behaviour of this structure under module homomorphisms, localizations, quotient modules, Cartesian product. Finally, we state two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are almost $S$-prime.https://jart.guilan.ac.ir/article_6769_3e4565fcd00a15dd5e41046a6ed28b8c.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601On Derivation Algebra Bundle4348677010.22124/jart.2023.22810.1422ENR.KumarDepartment of Mathematics School of Applied Sciences REVA University, Bangalore-
560064, IndiaJournal Article20220819We show that the radical bundle of an algebra bundle is a characteristic ideal bundle. Further we prove an algebra bundle is semisimple if and only if its derivation algebra bundle is either semisimple or zero.https://jart.guilan.ac.ir/article_6770_6020fc027aee46761c3c92ad263b363a.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601On a question concerning the Cohen's theorem4953630810.22124/jart.2022.22922.1432ENS. S.PourmortazaviDepartment of Mathematics, Guilan University, Rasht, IranS.KeyvaniDepartment of Mathematics, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali Branch, IranJournal Article20220914Let $R$ be a commutative ring with identity, and let $M$ be an $R$-module. The Cohen's theorem is the classic result that a ring is Noetherian if and only if its prime ideals are finitely generated. Parkash and Kour obtained a new version of Cohen's theorem for modules, which states that a finitely generated $R$-module $M$ is Noetherian if and only if for every prime ideal $p$ of $R$ with $Ann(M) \subseteq p$, there exists a finitely generated submodule $N$ of $M$ such that $pM \subseteq N \subseteq M(p)$, where $M(p) = \{x \in M | sx \in pM \,\,\textit{for some} \,\, s \in R \backslash p\}$. In this paper, we prove this result for some classes of modules. https://jart.guilan.ac.ir/article_6308_acf6ba066d294be0dfbf50fc5dbe6e30.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601Perfect 2-Colorings of Cn × Cm5563630610.22124/jart.2023.18779.1250ENM.AlaeiyanDepartment of Mathematics, Iran University of Science and Technology, Tehran, IranM.Kamran JamilDepartment of Mathematic, Riphah Institute of Computing and Applied Sciences (RICAS),
Riphah International University, 14 Ali Road, Lahore, PakistanMH.AlaeiyanFaculty of Computer Engineering, K. N. Toosi University of Technology, Seyed Khandan, , Tehran, Iran.Journal Article20210130In this paper, we enumerate the parameter matrices of all perfect 2-colorings of the generalized prism graph Cn × C3, where n ≥ 3,. We also present some generalized results for Cn × Cm, where m, n ≥ 3.https://jart.guilan.ac.ir/article_6306_1b5f32bc9728a7585e045a6ae8278efd.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601On pre-topological BCK-algebras6580679610.22124/jart.2023.22990.1439ENA. B.KhalafDepartment of Mathematics, University of Duhok, Duhok , Iraq0000-0002-9626-6908NehmatAhmedDepartment of Mathematics, College of Education, Salahaddin University, Erbil, IraqJournal Article20220926The concept of pre-open set in topological spaces was introduced by Mashhour \cite{ma} and the concept of BCK-algebras was defined by Iseki \cite{ise}. The aim of this paper is to supply the BCK-algebra by a topology that makes the operation defined on $X$ satisfy a special type of continuity with help of pre-open sets we call it p-topological BCK-algebra. This concept is an extension of the concept of topological BCK-algebra which was defined in \cite{dong}. By using properties of pre-open sets and axioms of BCK-algebras, several topological properties on BCK-algebras are found.https://jart.guilan.ac.ir/article_6796_4786aef61868aef537e77325b29183ee.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601Locally $\kappa$-presented representation of quiver8191679710.22124/jart.2023.23071.1447ENP.BahiraeiDepartment of Pure Mathematics
Faculty of Mathematical Sciences, University of Guilan
P. O. Box 41335-19141, Rasht, IranJournal Article20221016In this paper, we focus on the concept of locally $\kappa$-presented representations of quiver and we introduce two classes of objects of representations of the quiver on certain Grothendieck category related to this concept which forms a complete cotorsion pair.https://jart.guilan.ac.ir/article_6797_e325c33cd16bf8a916b5dd189122db12.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601On Graded $2$-absorbing Primary Hyperideals of a Graded Multiplicative Hyperring93109681710.22124/jart.2023.23135.1453ENP.GhiasvandDepartment of Mathematics, Payame Noor University(PNU), P.O.BOX 19395-3697 Tehran, Iran.Journal Article20221025Let $G$ be a group with identity $e$ and $R$ be a multiplicative hyperring. We introduce and study the notions of graded $2$-absorbing and graded $2$-absorbing primary hyperideals of a graded multiplicative hyperring $R$ which are generalizations of prime hyperideals. We present basic properties and characterizations of these graded hyperideals and homogeneous components. Among various results we prove that the intersection of two graded prime hyperideals is a graded $2$-absorbing hyperideal.https://jart.guilan.ac.ir/article_6817_2369d1f074140db4a0b8abdd38ec53a4.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601Study of multiplicative $b$-generalized derivation and its additivity111121681810.22124/jart.2023.23051.1444ENM. R.MozumderDepartment of
Mathematics, Aligarh Muslim University, Aligarh, India0000-0002-0350-9377W.AhmedDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaJournal Article20221012Our intention in this paper is to prove the following. Let R be a ring with an idempotent element (0, 1 ̸=)e and f be a multiplicative b-generalized derivation on R. Then we show that f is additive by<br />imposing certain conditions on the ring R.https://jart.guilan.ac.ir/article_6818_6d53e4aab3959d7206cbfb658a56de73.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601Single valued neutrosophic ideals of pseudo MV-algebras123136681910.22124/jart.2023.22952.1435ENR. A.BorzooeiDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran0000-0001-7538-7885M. AalyKologaniHatef Higher Education Institute, Zahedan, IranF.KarazmaDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti UniversityY. B.JunDepartment of Mathematics Education
Gyeongsang National University
Jinju 52828, Korea0000-0002-0181-8969Journal Article20220917After introducing the concept of single valued neutrosophic ideal in a pseudo MV-algebra, its properties are examined. The various conditions under which a single valued neutrosophic set can be a single valued neutrosophic ideal are examined. Characterizations of a single valued neutrosophic ideal of a pseudo MV-algebra are considered.https://jart.guilan.ac.ir/article_6819_6f12f1a4e85ac19b8b6e69ef8a0e0a23.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393111120230601On Lie ideals and symmetric bi-semiderivations in prime rings137146682010.22124/jart.2023.21465.1365END.YılmazErzurum Technical University, Faculty of Science, Department of Mathematics, Erzurum, Turkey0000-0002-6741-8669H.YazarlıDepartment of Mathematics, Sivas Cumhuriyet University Sivas, TurkeyJournal Article20220104In this paper, we investigate the relationship between symmetric bi-semiderivations and Lie ideals of a prime ring. Additionally, we extend some well-known results concerning symmetric biderivations of prime rings to symmetric bi-semiderivations.https://jart.guilan.ac.ir/article_6820_08bf823db54e78bbd9f35190bff295d1.pdf