Yazd UniversityAlgebraic Structures and Their Applications2382-976113320260801Module structures on $L$-algebras209227391910.22034/as.2025.23530.1816ENMonaAaly KologaniHatef Higher Education Institute, Zahedan, IranMohammadMohseni TakalloDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranRajab AliBorzooeiDepartment of Mathematics, Soft Computing and Artificial Intelligence Center, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran0000-0001-7538-7885Journal Article20250816In this paper, we apply the modules theory to $L$-algebras and introduce the concept of an $L$-module. Then we construct $L$-modules by using power sets and De Morgan algebras. Moreover, we investigate some properties of modules such as sub-module and other related results. Finally, we introduce the concepts of multiplication $L$-modules and co-multiplication $L$-modules and we will represent each sub-module of an $L$-module by using them.https://as.yazd.ac.ir/article_3919_5bf17f213fc4084b6cd8c2bc86653552.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976113320260801On prime ideals on a semi-ring associated with a nexus229248392010.22034/as.2025.23198.1796ENVajihehNazemi NiyaDepartment of Mathematics, Islamic Azad University of Kerman, Kerman, IranHojatBabaeiDepartment of Mathematics, Islamic Azad University of Kerman, Kerman, IranAkbarRezaeiDepartment of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran0000-0002-6003-3993Journal Article20250526In this study, we explore prime ideals and prime elements within a semi-ring constructed over a nexus. We characterize these elements using panels and quasi-panels. Furthermore, we establish conditions under which a semi-ring associated with a nexus $N$ becomes unitary. The concept of homomorphism for these semi-rings is introduced, and several of their properties are examined. Additionally, by analyzing their characteristics, we demonstrate that a quotient semi-ring can be induced by an ideal of a semi-ring over a nexus, and localization is successfully defined. To illustrate these concepts, we provide specific examples.https://as.yazd.ac.ir/article_3920_624a76412af82ade30fe44002d40bdca.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976113320260801A new class of dual notions: $S$-co-$r$-submodules and $S$-co-$n$-submodules based on multiplicatively closed subsets249260392910.22034/as.2025.23319.1803ENFarkhondeFarzalipourDepartment of Mathematics, Payame Noor University, P.O.BOX 19395-3697, Tehran, IranPeymanGhiasvandDepartment of Mathematics, Payame Noor University, P.O.BOX 19395-3697, Tehran, Iran0000-0003-4084-7057Journal Article20250627Let $R$ be a commutative ring, $M$ be an $R$-module and $S\subseteq R$ be a multiplicatively closed subset of $R$. The purpose of this paper is to introduce and investigate the concepts of $S$-co-$r$-submodules and $S$-co-$n$-submodules by using the notion of a multiplicatively closed subset of $R$. A non-zero submodule $N$ of $M$ with $Rad(Ann(M))\cap S=\emptyset$ is called an $S$-co-$n$-submodule, if there exists $s\in S$ such that whenever $aN\subseteq K$ and $sa\not \in Rad(Ann(M))$ for some $a\in R$ and a submodule $K$ of $M$, then $sN\subseteq K$. Many properties and examples are given of such submodules. Also, we state the correspondence between $S$-co-$r$-submodules and $S$-co-$n$-submodules.<br /> https://as.yazd.ac.ir/article_3929_49f745542516c191831f36ec4c5b1a4e.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976113320260801Structure of linear codes invariant under the unitary group $U(3,3)$261278400410.22034/as.2026.22222.1744ENTapiwanashe GiftNyikadzinoDepartment of Mathematics and Applied Mathematics, Faculty of Science and Agriculture, University of Limpopo, Turfloop, Polokwane, South Africa.0000-0001-5531-294XAminSaeidiDepartment of Mathematics and Applied Mathematics, Faculty of Science and Agriculture, University of Limpopo, Turfloop, Polokwane, South Africa.Thekiso TrevorSeretloSchool of Mathematical and Statistical Sciences, PAA Focus Area, Faculty of Natural Sciences, North-West University, Mabatho, Mafikeng, South Africa.Journal Article20241003In this paper, we outline a method for constructing linear codes invariant under primitive permutation groups. We will demonstrate that when a group $G$ possesses a trivial Schur multiplier, every binary linear code that admits $G$ as a permutation group can be regarded as a submodule of the permutation module within the primitive action of $G$. As an illustrative example, we select the finite simple group $G = U(3,3)$ and identify the complete set of linear codes derived from its 2-representations.<br />In addition, we use the supports of the codewords to construct certain designs that remain invariant under the action of $U(3,3)$ and establish connections between these designs and the corresponding linear codes.https://as.yazd.ac.ir/article_4004_970f132ae81b89dd92523e4bf452350e.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976113320260801Finite groups with some $\mathcal{HC}-$subgroups279289402710.22034/as.2026.21919.1731ENMohamed RamadanShahinDepartment of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.0009-0007-1985-7791Journal Article20240721Let $G$ be a finite group. A subgroup $H$ of $G$ is called an $\mathcal{H}{-}$subgroup in $G$ if $H^{g}\cap N_{G}(H)\leq H$ for all $g\in G.$ A subgroup $H$ of $G$ is called an $\mathcal{H}{ C-}$subgroup in $G$ if there exists a normal subgroup $T$ of $G$ such that $G=HT$ and $H^{g}\cap N_{T}(H)\leq H$ for all $g\in G.$ In this paper, we give some new criteria for $p-$nilpotency and supersolvability of a group $G$ when certain subgroups of prime power orders of $G$ are $\mathcal{H}{ C-}$subgroups.https://as.yazd.ac.ir/article_4027_c0480c372142d22777f8bf145c95a11b.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976113320260801The effect of the sum of the inverse-power of element orders on finite groups291301414210.22034/as.2026.22786.1773ENSaraPooyandehDepartment of Mathematics, Payamenoor University, Tehran, Iran.0000-0002-2365-0917LalehOftadehDepartment of Mathematics, Fir. C., Islamic Azad University, Firoozabad,
Iran.Journal Article20250211Let $G$ be a finite group, and let $m(G)=\sum_{g \in G}1/o(g)$, where $o(g)$ denotes the order of $g$. In this paper, we determine all groups such that $m(G)<4$. Additionally, for a finite group $G$ of odd order, we investigate the influence of $m(G)$ on supersolvability. Finally, we provide a criterion for $p$-solvability using the function $m(G)$, where $ p \in \{7,11\}$.https://as.yazd.ac.ir/article_4142_aabeb0eb6c5de7913dd2b34b6ed6dd52.pdf