Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 Directed prime graph of non-commutative ring 1 12 1963 10.29252/as.2021.1963 EN Sanjoy Kalita Department of Mathematics, Gauhati University, Guwahati- 781014, Assam, India 0000-0002-9670-1578 Kuntala Patra Department of Mathematics, Gauhati University, Guwahati- 781014, Assam, India Journal Article 2020 08 09 Prime 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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 Limits and colimits in the category of pre-directed complete pre-ordered sets 13 23 1833 10.29252/as.2020.1833 EN Halimeh Moghbeli Depatment of Mathematcs, Faculty of science, University of Jiroft, Jiroft, Iran Journal Article 2019 10 30 In 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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 On \$mathbb{Z}G\$-clean rings 25 40 1834 10.29252/as.2020.1834 EN Marzieh Farmani Islamic Azad university, Roudehen branch, Roudehen, Iran. Journal Article 2018 06 19 Let \$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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 Boolean expression based on hypergraphs with algorithm 41 60 1835 10.29252/as.2020.1835 EN Mohammad Hamidi Department of mathematics, Payame Noor university, Tehran, Iran. 0000-0002-8686-6942 Marzieh Rahmati Department of mathematics, Payame Noor university, Tehran, Iran. Akbar Rezaei Department of Mathemtics, Payame Noor University, Tehran, Iran 0000-0002-6003-3993 Journal Article 2020 07 17 This 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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 \$r\$-Submodules and \$uz\$-modules 61 73 1858 10.29252/as.2020.1858 EN Rostam Mohamadian Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Journal Article 2020 03 03 In 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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 Generalized stone residuated lattices 75 87 1885 10.29252/as.2020.1885 EN Saeed Rasouli Department of Mathematics, College of science, Persian Gulf University, Bushehr, 7516913817, Iran Journal Article 2019 09 15 This 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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 Modules whose nonzero finitely generated submodules are dense 89 97 1908 10.29252/as.2020.1908 EN Alireza Hajikarimi Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Isfahan, Iran, Journal Article 2020 09 24 Let \$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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 Some classical theorems in state residuated lattices 99 116 1910 10.29252/as.2020.1910 EN Mohammad Taheri Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran. Farhad Khaksar Haghani Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran. Saeed Rasouli Department of Mathematics, Persian Gulf University, Bushehr, Iran. Journal Article 2020 01 09 This 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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 On the small intersection graph of submodules of a module 117 130 1936 10.29252/as.2020.1936 EN Lotf Ali Mahdavi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran 0000-0002-9560-432X Yahya Talebi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran Journal Article 2020 07 11 Let \$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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 A new approach to smallness in hypermodules 131 145 1962 10.29252/as.2020.1962 EN Ali Reza Moniri Hamzekolaee Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran 0000-0002-2852-7870 Morteza Norouzi Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran Violeta Leoreanu-Fotea Faculty of Mathematics, University of Al.I. Cuza of Iasi, Iasi, Romania Journal Article 2020 07 03 In 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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 Generalization of reduction and closure of ideals 147 161 1957 10.29252/as.2020.1957 EN Jafar Azami Department of Mathematics, Faculty of Science, University of mohaghegh Ardabili, Ardabil Maryam Khajepour Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran Journal Article 2019 12 10 Throughout 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.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 8 1 2021 02 01 Left \$phi\$-biprojectivity of some classes of abstract Segal algebras 163 171 1960 10.29252/as.2020.1960 EN Amir Sahami Department of Mathematics, Faculty of Basic Sciences, Ilam University P.O. Box 69315- 516 Ilam, Iran. 0000-0003-0041-509X Journal Article 2020 09 15 In 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