Yazd UniversityAlgebraic Structures and Their Applications2382-97618120210201Directed prime graph of non-commutative ring112196310.29252/as.2021.1963ENSanjoyKalitaDepartment of Mathematics, Gauhati University, Guwahati- 781014, Assam, India0000-0002-9670-1578KuntalaPatraDepartment of Mathematics, Gauhati University, Guwahati- 781014, Assam, IndiaJournal Article20200809Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$. Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the paper.http://as.yazd.ac.ir/article_1963_a086ffe2ea7f78db35c78e98cb91fb1a.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201Limits and colimits in the category of pre-directed complete pre-ordered sets1323183310.29252/as.2020.1833ENHalimehMoghbeliDepatment of Mathematcs, Faculty of science, University of Jiroft, Jiroft, IranJournal Article20191030In this paper, some categorical properties of the category { Pre-Dcpo} of all pre-dcpos; pre-ordered sets which are also pre-directed complete, with pre-continuous maps between them is considered. In particular, we characterize products and coproducts in this category. Furthermore, we show that this category is neither complete nor cocomplete. Also, epimorphisms and monomorphisms in {Pre-Dcpo} are described.<br />Finally, some adjoint relations between the category {Pre-Dcpo} and others are considered.<br />More precisely, we consider the forgetful functors between this category and some well-known categories, and study the existence of their left and right adjoints.http://as.yazd.ac.ir/article_1833_1404f3ce63532e68b6cababfef034fbb.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201On $mathbb{Z}G$-clean rings2540183410.29252/as.2020.1834ENMarziehFarmaniIslamic Azad university, Roudehen branch, Roudehen, Iran.Journal Article20180619Let $R$ be an associative ring with unity. An element $x in R$ is called $mathbb{Z}G$-clean if $x=e+r$, where $e$ is an idempotent and $r$ is a $mathbb{Z}G$-regular element in $R$. A ring $R$ is called $mathbb{Z}G$-clean if every element of $R$ is $mathbb{Z}G$-clean. In this paper, we show that in an abelian $mathbb{Z}G$-regular ring $R$, the $Nil(R)$ is a two-sided ideal of $R$ and $frac{R}{Nil(R)}$ is $G$-regular. Furthermore, we characterize $mathbb{Z}G$-clean rings. Also, this paper is involved with investigating $mathbb{F}_{2}C_{2}$ as a social group and measuring influence a member of it’s rather than others.http://as.yazd.ac.ir/article_1834_b47925092dd71dacb9f2c4aa272f4c4f.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201Boolean expression based on hypergraphs with algorithm4160183510.29252/as.2020.1835ENMohammadHamidiDepartment of mathematics, Payame Noor university, Tehran, Iran.0000-0002-8686-6942MarziehRahmatiDepartment of mathematics, Payame Noor university, Tehran, Iran.AkbarRezaeiDepartment of Mathemtics, Payame Noor University, Tehran, Iran0000-0002-6003-3993Journal Article20200717This paper introduces a novel concept of Boolean function--based hypergraph with respect to any given T.B.T(total binary truth table). This study defines a notation of kernel set on switching functions and proves that every T.B.T corresponds to a Minimum Boolean expression via kernel set and presents some conditions on T.B.T to obtain a Minimum irreducible Boolean expression from switching functions. Finally, we present an algorithm and so Python programming(with complete and original codes) such that for any given T.B.T, introduces a Minimum irreducible switching expression.http://as.yazd.ac.ir/article_1835_f314ebb3e757a37b7bc9fbc25a2616bd.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201$r$-Submodules and $uz$-modules6173185810.29252/as.2020.1858ENRostamMohamadianDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Journal Article20200303In this article we study and investigate the behavior of $r$-submodules (a proper submodule $N$ of an $R$-module $M$ in which $amin N$ with ${rm Ann}_M(a)=(0)$ implies that $min N$ for each $ain R$ and $min M$). We show that every simple submodule, direct summand, divisible submodule, torsion submodule and the socle of a module is an $r$-submodule and if $R$ is a domain, then the singular submodule is an $r$-submodule. We also introduce the concepts of $uz$-module (i.e., an $R$-module $M$ such that either ${rm Ann}_M(a)not=(0)$ or $aM=M$, for every $ain R$) and strongly $uz$-module (i.e., an $R$-module $M$ such that $aMsubseteq a^2M$, for every $ain R$) in the category of modules over commutative rings. We show that every Von Neumann regular module is a strongly $uz$-module and every Artinian $R$-module is a $uz$-module. It is observed that if $M$ is a faithful cyclic $R$-module, then $M$ is a $uz$-module if and only if every its cyclic submodule is an $r$-submodule. In addition, in this case, $R$ is a domain if and only if the only $r$-submodule of $M$ is zero submodule. Finally, we prove that $R$ is a $uz$-ring if and only if every faithful cyclic $R$-module is a $uz$-module.http://as.yazd.ac.ir/article_1858_e56137168d963b0cd59264b32a0409e8.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201Generalized stone residuated lattices7587188510.29252/as.2020.1885ENSaeedRasouliDepartment of Mathematics, College of science, Persian Gulf University, Bushehr, 7516913817, IranJournal Article20190915This paper introduces and investigates the notion of a generalized Stone residuated lattice. It is observed that a residuated lattice is generalized Stone if and only if it is quasicomplemented and normal. Also, it is proved that a finite residuated lattice is generalized Stone if and only if it is normal. A characterization for generalized Stone residuated lattices is given by means of the new notion of $alpha$-filters. Finally, it is shown that each non-unit element of a directly indecomposable generalized Stone residuated lattice is a dense element.http://as.yazd.ac.ir/article_1885_0b9b070512dcc251b97fb58d50f28bd9.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201Modules whose nonzero finitely generated submodules are dense8997190810.29252/as.2020.1908ENAlirezaHajikarimiDepartment of Mathematics, Mobarakeh Branch, Islamic Azad University, Isfahan, Iran,Journal Article20200924Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. First, we study multiplication $R$-modules $M$ where $R$ is a one dimensional Noetherian ring or $M$ is a finitely generated $R$-module. In fact, it is proved that if $M$ is a multiplication $R$-module over a one dimensional Noetherian ring $R$, then $Mcong I$ for some invertible ideal $I$ of $R$ or $M$ is cyclic. Also, a multiplication $R$-module $M$ is finitely generated if and only if $M$ contains a finitely generated submodule $N$ such that $Ann_R(N)= Ann_R(M)$. A submodule $N$ of $M$ is called dense in $M$, if $M=sum_varphivarphi(N)$ where $varphi$ runs over all the $R$-homomorphisms from $N$ into $M$ and $R$-module $M$ is called a weak $pi$-module if every non-zero finitely generated submodule is dense in $M$. It is shown that a faithful multiplication module over an integral domain $R$ is a weak $pi$-module if and only if it is a Prufer prime module.http://as.yazd.ac.ir/article_1908_03d715782fe4c57fe51ab46c105689b6.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201Some classical theorems in state residuated lattices99116191010.29252/as.2020.1910ENMohammadTaheriDepartment of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.FarhadKhaksar HaghaniDepartment of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.SaeedRasouliDepartment of Mathematics, Persian Gulf University, Bushehr, Iran.Journal Article20200109This paper, by considering the notion of a state residuated lattice morphism in the class of state residuated lattices, investigates some classical theorems namely the going up and lying over theorems. Results show that each state residuated lattice morphism fulfills these theorems. Also, some properties about prime filters of residuated lattices are obtained which are given in the paper.http://as.yazd.ac.ir/article_1910_a72d5bbf47f72d3bd4e138cee3f407ef.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201On the small intersection graph of submodules of a module117130193610.29252/as.2020.1936ENLotf AliMahdaviDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran0000-0002-9560-432XYahyaTalebiDepartment of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, IranJournal Article20200711Let $M$ be a unitary left $R$-module, where $R$ is a (not necessarily commutative) ring with identity. The small intersection graph of nontrivial submodules of $M$, denoted by $Gamma(M)$, is an undirected simple graph whose vertices are in one-to-one correspondence with all nontrivial submodules of $M$ and two distinct vertices are adjacent if and only if the intersection of corresponding submodules is a small submodule of $M$. In this paper, we investigate the fundamental properties of these graphs to relate the combinatorial properties of $Gamma(M)$ to the algebraic properties of the module $M$. We determine the diameter and the girth of $Gamma(M)$. We obtain some results for connectivity and planarity of these graphs. Moreover, we study orthogonal vertex, domination number and the conditions under which the graph $Gamma(M)$ is complemented.http://as.yazd.ac.ir/article_1936_549005a289b7997dd54a242798ddba46.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201A new approach to smallness in hypermodules131145196210.29252/as.2020.1962ENAli RezaMoniri HamzekolaeeDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran0000-0002-2852-7870MortezaNorouziDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, IranVioletaLeoreanu-FoteaFaculty of Mathematics,
University of Al.I. Cuza of Iasi,
Iasi, RomaniaJournal Article20200703In this paper, we extend the concept of small subhypermodules to all types of hypermodules and give nontrivial examples for this concept. As an application, we define and study lifting hypermodules via small subhypermodules.http://as.yazd.ac.ir/article_1962_0993a1d16853a36bb399fc654f3691a1.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201Generalization of reduction and closure of ideals147161195710.29252/as.2020.1957ENJafarAzamiDepartment of Mathematics, Faculty of Science, University of mohaghegh Ardabili, ArdabilMaryamKhajepourDepartment of Mathematics, University of Mohaghegh Ardabili, Ardabil, IranJournal Article20191210Throughout this paper, all rings are commutative with identity and all modules are unital. Let $R$ be a ring and $M$ be an $R$-module. Then $M$ is called a multiplication module provided for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N=IM$. Also $M$ is said to be a comultiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $ N=(0:_MI)$. In this paper, we introduce the notions of reduction and coreduction of submodules, integral dependence, integral codependence, integral closure and $Delta$-closure over multiplication and comultiplication modules.http://as.yazd.ac.ir/article_1957_96c2f28af0a068d3668aa25c8f59db1a.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618120210201Left $phi$-biprojectivity of some classes of abstract Segal algebras163171196010.29252/as.2020.1960ENAmirSahamiDepartment of Mathematics, Faculty of Basic Sciences, Ilam University P.O. Box 69315-
516 Ilam, Iran.0000-0003-0041-509XJournal Article20200915In this paper, we investigate left $phi$-biprojectivity of Segal algebras and abstract Segal algebras. We show that for some abstract Segal algebras with some mild conditions left $phi$-biprojectivity is equivalent with left $phi$-contractibility. Also, we characterize left $phi$-biprojectivity of a Segal algebra $S(G)$ in the terms of compactness of $G,$ where $G$ is a locally compact group. We introduce a class of abstract Segal algebras among Triangular Banach algebras. We show that some abstract Segal algebras related to triangular Banach algebras are not biprojective.http://as.yazd.ac.ir/article_1960_d2b8d0281bbce196a7ee7554c9bb9353.pdf