University of GuilanJournal of Algebra and Related Topics2345-393114120260801The relationships of Ivar(G) with Inner automorphisms in S(G)-autonilpotent groups114952310.22124/jart.2026.29119.1737ENS.BarinDepartment of Mathematics, University of Birjand, Birjand, IranM. M.NasrabadiDepartment of Mathematics, University of Birjand, Birjand, IranJournal Article20241129Bachmuth defined an IA-automorphism of a group G as an automorphism of G which induces the identity automorphism on G/G'. Ghumde and Ghate introduced S(G) and Ivar(G) subgroups. In this paper, we first introduce a new series on the IA-central subgroup and verify the relationships of the members of this series. Also, we give a new definition for S(G)-autonilpotency on this series. Then, we discuss some properties of these concepts with some theorem and their corollaries. We investigate the members of Ivar(G) fixing the center element-wise. At the end of this paper, we study the conditions in which Ivar(G) relate to Inner automorphisms in S(G)-autonilpotent groups. https://jart.guilan.ac.ir/article_9523_f3f696e616f69e2d34e7d80a38f1d543.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Super-biderivations and linear super-commuting maps on infinite-dimensional Lie superalgebras1536928510.22124/jart.2025.29499.1755ENM.AbdaouiUniversity of Kairouan, LR18ES45, Mathematical Physics, Quantum Modeling and Mechanical Design,Preparatory Institute for Engineering Studies of Kairouan, Kairouan, 3100, TunisiaJournal Article20250106Let $\mathcal{G}_{\epsilon}$ (resp. $\mathcal{W}_{\epsilon}$) with $\epsilon=0$ or $\frac{1}{2}$ be the complete spectrum-generating superalgebra (resp. the centerless super Virasoro algebra). In this paper, the super-skewsymmetric super-biderivations on $\mathcal{G}_{\epsilon}$ and $\mathcal{W}_{\epsilon}$ are completely determined. In particular, we show that every super-skewsymmetric super-biderivation $\varphi$ (resp. $\phi$) of $\mathcal{G}_{\epsilon}$ (resp. $\mathcal{W}_{\epsilon}$) is inner. Based on the results of super-biderivations, we shall give the certain forms of all linear super-commuting maps on $\mathcal{G}_{\epsilon}$ and $\mathcal{W}_{\epsilon}$https://jart.guilan.ac.ir/article_9285_6f9043c70193b85606cebef2a86fdd0e.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801On a generalization of regular rings with central nilpotents3748885310.22124/jart.2025.29309.1748ENSh.RahimiDepartment of Mathematics, College of Sciences, Shiraz University, Shiraz, IranB.AminiDepartment of Mathematics, College of Sciences, Shiraz University, Shiraz, IranA.AminiDepartment of Mathematics, College of Sciences, Shiraz University, Shiraz, IranH.SharifDepartment of Mathematics, College of Sciences, Shiraz University, Shiraz, IranJournal Article20241220A ring $R$ is called $\pi$-regular if, for every $x\in R$, there exists $y\in R$ such that $x^n=x^nyx^n$ for some positive integer $n$. Here, we shall give some characterizations of $\pi$-regular rings in which nilpotent elements lie in the center. It is shown that these rings can be formulated in a way motivated by recent works of P. Danchev, leading to new insights into $\pi$-regular rings and providing partial answers to a question posed by him. In the end, we aim to classify this class of rings, up to an isomorphism.https://jart.guilan.ac.ir/article_8853_99d5877cf5b2ea8fff67fe910927b902.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801On Hom-Jacobi algebra structures4968931810.22124/jart.2025.28806.1726ENR. R.Moulengou NkomboFacult\'e des Sciences et Techniques, Universit\'e Marien Ngouabi, Brazzaville, CongoN.Mahoungou MoukalaEcole Normale Sup\'erieure, Universit\'e Marien Ngouabi, Brazzaville, CongoJournal Article20241026We define hom-Jacobi algebras as an extension of hom-Poisson algebras and we give some examples. We describe the universal property of first-order hom-differential operators as well as the universal property of first-order hom-differential multi-operators. By using these universal properties, we prove the existence and uniqueness of a canonical purely hom-Jacobi form associated to purely hom-Jacobi algebra.https://jart.guilan.ac.ir/article_9318_34de5d97c11248d2a494df89a77f1824.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Line comaximal graphs6975832610.22124/jart.2025.28997.1732ENS.KhojastehDepartment of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, IranJournal Article20241116Let $R$ be a commutative ring with non-zero identity. The comaximal graph is a graph with vertices all<br />elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $Rx +Ry = R$. Let $\Gamma_2(R)$ be the subgraph of the comaximal graph with vertex-set $W^{*}(R)$, where $W^{*}(R)$ is the set of all non-zero and non-unit elements of $R$. In this paper, we investigate when the graph $\Gamma_2(R)$ is a line graph. We completely present all commutative rings which their comaximal graphs are line graphs. Also, we study when the comaximal graph is the complement of a line graph.https://jart.guilan.ac.ir/article_8326_6227ef5ad10310acae6026b913ff8d11.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Ring in which every element is sum of two $6-$potent elements7786820410.22124/jart.2024.26096.1605ENK. N.DekaDepartment of Mathematics, Gauhati University, Guwahati, IndiaH. K.SaikiaDepartment of Mathematics, Gauhati University, Guwahati, IndiaJournal Article20231123In this paper, we prove the following results. Every element of a ring $R$ is a sum of two commuting $6-$potent elements if and only if $R$ is isomorphic to $R_1\times R_2\times R_3$, where $R_1$ is isomorphic to a subdirect product of $Z_2$'s, $R_2$ is isomorphic to a subdirect product of $Z_3$'s and $R_3$ is isomorphic to a subdirect product of $Z_{11}$'s. Also, if every element of a ring $R$ is the sum of two 6-potent and one nilpotent all commute with each other, then $R$ is isomorphic to $R_1\times R_2\times R_3$, where $J(R_1)$ is nil and $R_1/J(R_1)$ is a subdirect product of rings isomorphic to either of the rings $Z_2,F_4,M_2(F_2)$ and $M_2(F_4)$ , $a^{81}-a$ is nilpotent for every $a\in R_2$ , $J(R_3)$ is nil and $R_3/J(R_3)$ is a subdirect product of $Z_{11}$'s.https://jart.guilan.ac.ir/article_8204_6eb634067765250dea5af09df5231d0f.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Ordered right (left) quasi-adequate semigroups87114943210.22124/jart.2026.29076.1735ENA.El-QallaliDepartment of Mathematics, Faculty of Science, University of Tripoli, LibyaJournal Article20241123In this paper, we provide a structure theorem for a naturally ordered quasi-adequate semigroup $(S,\leq)$ with a maximum idempotent $u$ in which $uSu$ is an adequate subsemigroup of $S$ with the property that the relations $\L$ and $\R$ are abundant.https://jart.guilan.ac.ir/article_9432_e4494c6b16f655188dfa439b69df4ce6.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Complemented and completely regular $\Gamma-$ semirings115126932010.22124/jart.2025.29305.1747ENT. R.SharmaHimachal Pradesh University Regional Centre, Dharamshala (H.P.), IndiaR.KumarGovernment Degree College, Dharamshala(H.P.), IndiaJournal Article20241220This paper investigates the additive and multiplicative properties of complemented and completely regular $\Gamma-$ semirings. We prove many results on different structures of $\Gamma-$ semirings like anti-inverse, quasi-separative, distributive, and partial order. Boolean $\Gamma-$ semiring is demonstrated by applying the concept of a completely regular $\Gamma-$ semiring. Finally, by using the idea of simple and completely regular $\Gamma-$ semiring, we define a relation $\leq$ on $R$ such that $x \leq y$ if and only if $x+y+1 = x\alpha y$ for all $x,y \in R, \alpha \in \Gamma $ and prove that $R$ is a partially ordered $\Gamma-$ semiring.https://jart.guilan.ac.ir/article_9320_cffe0b22864d9c0b1f783fbb121e15ae.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Monoid rings and the McCoy's theorem127135931910.22124/jart.2025.29511.1756ENM.HabibiDepartment of Mathematics, Tafresh University, Tafresh, IranK.PaykanDepartment of Mathematics, Tafresh University, Tafresh, IranJournal Article20250107Let $M$ be a nilpotent quotient of a free monoid. satisfying the monoid ring $R[M]$ in the McCoy's theorem for any semiprime or right APP ring $R$ is proven. Also, it is shown that $R[M]$ is right McCoy for any reduced ring $R$.https://jart.guilan.ac.ir/article_9319_38d3759ebddeb98a341295b96a4b19e4.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801On the continued fraction expansions of some transcendental series in $\mathbb{F}_{q}((T^{-1}))$137146832710.22124/jart.2025.28559.1718ENS.BELDILab. AGTS, University of Sfax, 3000 Sfax, TunisiaF.TaktakLab. AGTS, University of Sfax, 3000 Sfax, TunisiaJournal Article20240926In this paper we describe the continued fraction expansions of certain infinite series over $\mathbb{F}_{q}(T)$, where $\mathbb{F}_{q}$ is a finite field with $q$ elements. As the first application, we determine the continued fraction expansion of the sum of rational functions with exponential elements. As the second application, we exhibit the continued fraction expansions of many classes of transcendental series that have bounded partial quotients.https://jart.guilan.ac.ir/article_8327_e72f3a499eff1bf8c55811112b476960.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Zero-divisor graphs of semirings with no S-vertices147157928410.22124/jart.2025.29182.1740ENE.Mehdi-NezhadDepartment of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Cape Town, South AfricaK. O. E.HassanDepartment of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Cape Town, South AfricaJournal Article20241206Let $R$ be a commutative semiring (ring) with identity $1 \neq 0$. A vertex $a$ in a simple graph $G$ is said to be a Smarandache vertex (or S-vertex for short) provided that there exist three distinct vertices $x$, $y$, and $b$ (all different from $a$) in $G$ such that $x$---$a$, $a$---$b$, and $b$---$y$ are edges in $G$, but there is no edge between $x$ and $y$. In this interdisciplinary subject, we investigate the interplay between the algebraic properties of the commutative semirings and their associated zero-divisor graphs, denoted by $\Gamma(R)$, using the notion of the S-vertices in connection with the nonexistence of S-vertices in $\Gamma(R)$. We discuss when $\Gamma(R)$ is a complete bipartite graph together with some of its other graph-theoretic properties and their relation to the nonexistence of S-vertices of $\Gamma(R)$.https://jart.guilan.ac.ir/article_9284_0f3b9542d3d7effdc7cd0c648452d669.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801The generators of total multiplication group of Cheban loop159182959710.22124/jart.2026.28508.1717ENB.OsobaDepartment of Physical Sciences, Bells University of Technology, Ota, Ogun State, NigeriaT. G.JaiyeolaDepartment of Mathematics, Obafemi Awolowo University, Ile Ife 220005, Nigeria
Department of Mathematics, University of Lagos, Akoka, NigeriaL. O.AdekolaDepartment of Physical Sciences, Bells University of Technology, Ota, Ogun State, NigeriaM. T.AdenibuyanDepartment of Computer Science, Bells University of Technology, Ota, Ogun State, NigeriaJournal Article20240920A Cheban loop $(G, \circ)$ is characterized by the identities $(z\circ yx)x= zx\circ xy$ and $x(xy\circ z)= yx\circ xz$ for all $x,y,z\in G$. It was established that the left, right, and middle nuclei of a Cheban loop coincide, and the nucleus of a Cheban loop is the set of elements $a$ whose middle inner mappings $T_a$ are automorphisms. The generators of the inner mapping group of a Cheban were refined in terms of one of the generators of the total inner mapping group of a Cheban loop. Necessary and sufficient conditions regarding the inner mapping group (associators) for a loop to be a Cheban loop were established. It was shown that, in a Cheban loop, the mapping $a\mapsto T_a$ is an endomorphism if and only if the left (right) inner mapping is a left (right) regular mapping. Additionally, a Cheban loop was proved to be a left and right automorphic loop and that the left and right inner mappings belong to its middle inner mapping group. Furthermore, a Cheban loop was shown to be an automorphic loop (A-loop) if and only if it is a middle automorphic loop (middle A-loop). Some interesting relations involving the generators of the total multiplication group and total inner mapping group of a Cheban loop were derived, and based on these, the generators of the total inner mapping group of a Cheban loop were fine-tuned. Finally, it was shown that a Cheban loop is a totally automorphic loop (TA-loop) if and only if it is a commutative and flexible loop. These results above were used to give a partial answer to a 2013 question and an apparent solution to the 2015 problem in the case of a Cheban loop.https://jart.guilan.ac.ir/article_9597_ebad13f94871f645d870e2c4c184775a.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Saturated and absolutely closed posemigroups183198945810.22124/jart.2026.29417.1751ENS. A.AhangerDepartment of Mathematics, Central University of Kashmir, Ganderbal, IndiaS. A.MirDesh Bhagat University, Punjab, IndiaA. H.BhatGoverment Degree College Shopian, Jammu and Kashmir, IndiaJournal Article20241229We show that commutative inverse posemigroups and finite monogenic posemigroups are saturated in the category of all posemigroups. Further, we show that the variety of pobands satisfying the identity $axya=ayxa$ is closed as well as saturated. Finally, we show that the convex finite monogenic posemigroups and inverse posemigroups are absolutely closed in the category of all commutative posemigroups.https://jart.guilan.ac.ir/article_9458_a862bf9c1496c620116e009352efe877.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801Non-identity order divisor graphs of groups199206884910.22124/jart.2025.28373.1716ENM.SattanathanDepartment of Mathematics, Sri Paramakalyani College, Alwarkurichi,Tamil Nadu, IndiaJ.KottarathilDepartment of Mathematics, St. Joseph’s College (Autonomous), Devagiri, Kozhikode, Kerala, IndiaI.ChakrabartyDepartment of Mathematics, CHRIST(Deemed to be University), Bengaluru, IndiaJournal Article20240917Let $G$ be a group with identity $e$. In this paper, we define and study the non-identity order divisor graph of $G$, where the vertex set is $G-\{e\}$ and two distinct vertices $x$ and $y$ are adjacent if and only if either $O(x)|O(y)$ or $O(y)|O(x)$. We denote the order divisor graph of group $G$ by $\o(G)$. We study some basic properties of $\o(G)$ such as connectedness, completeness, bipartiteness and Eulerian property. The lower bound as well as the number of edges of $\o(G)$ are also calculated for some group $G$ and some characterizations for fundamental properties of $\o(G)$ have been obtained. Finally, we explore the relation between the order prime graph and the non-identity order divisor graph of some group $G$.https://jart.guilan.ac.ir/article_8849_e8d604a91728265e048feeedb0bfa897.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393114120260801On intuitionistic L-fuzzy PMS-ideals in PMS-algebras207226980910.22124/jart.2026.28223.1701ENB. L.DersehDepartment of Mathematics, College of Natural and Computational Science, Debre Markos University, Debre Markos, Ethiopia0000-0002-7726-5248Journal Article20240820In this paper, we apply the concept of an intuitionistic L-fuzzy set to PMS-ideals of PMS-algebras. The notion of the intuitionistic L-fuzzy PMS-ideal of a PMS-algebra is introduced and several associated properties are investigated. A condition for an intuitionistic L-fuzzy set in a PMS-algebra to be an intuitionistic L-fuzzy PMS-ideal is established. Characterizations of intuitionistic L-fuzzy PMS-ideals of a PMS-algebra in terms of their level subsets are given. The algebraic nature of intuitionistic L-fuzzy PMS-ideals of a PMS-algebra under homomorphism is discussed. Moreover, the Cartesian product of the intuitionistic L-fuzzy PMS-ideals of a PMS-algebra is also studied and some interesting results are obtained. Finally, the relationship between the strongest intuitionistic L-fuzzy relations in a PMS-algebra and intuitionistic L-fuzzy PMS-ideals of a PMS-algebra are explored.https://jart.guilan.ac.ir/article_9809_f2719d743b7e3e04c8fb68e547f3023a.pdf