Yazd UniversityAlgebraic Structures and Their Applications2382-97617120200201On the associated primes of the generalized $d$-local cohomology modules110161510.22034/as.2020.1615ENZahraRahimi-molaeiDepartment of Mathematics, Imam Khomeini International University, Qazvin, IranShiroyehPayroviDepartment of Mathematics, Imam Khomeini International
University, Qazvin, Iran.SakinehBabaeiDepartment of mathematics, Imam Khomeini International University, Qazvin, Iran0000-0001-7039-2095Journal Article20190427The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary generalized local cohomology modules. Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$ are finitely generated $R$-modules and $d, t$ are two integers. We prove that $\Ass H^t_d(M,N)=\bigcup_{I\in \Phi} \Ass H^t_I(M,N)$ whenever $H^i_d(M,N)=0$ for all $i< t$ and $\Phi=\{I: I \text{ is an ideal of}\ R \text{ with}\ \dim R/I\leq d \}$. In the second part of the paper, we give some information about the non-vanishing of the generalized $d$-local cohomology modules. To be more precise, we prove that $H^i_d(M,R)\neq 0$ if and only if $i=n-d$ whenever $R$ is a Gorenstein ring of dimension $n$ and $pd_R(M)<\infty$. This result leads to an example which shows that $\Ass H^{n-d}_d(M,R)$ is not necessarily a finite set.https://as.yazd.ac.ir/article_1615_a0870992cd28c1d8c56ed39c2806d814.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201Cofinitely weak generalized $\delta$-supplemented modules1120162010.22034/as.2020.1620ENBehnamTalaeeDepartment of Math. Faculty of Basic Science, Babol Noshirvani University of technology, Babol, Iran0000-0002-1394-4866Journal Article20190514We will study modules whose cofinite submodules have weak generalized-$\delta$-supplements. We attempt to investigate some properties of cofinitely weak generalized $\delta$-supplemented modules. We will prove for a module $M$ and a semi-$\delta$-hollow submodule $N$ of $M$ that, $M$ is cofinitely weak generalized $\delta$-supplemented if and only if $\frac{M}{N}$ is cofinitely weak generalized $\delta$-supplemented. Also we show that any $M$-generated module is cofinitely weak generalized $\delta$-supplemented module, where $M$ is cofinitely weak generalized $\delta$-supplemented. We obtain some other results about this kind of modules.<br />We will study modules whose cofinite submodules have weak generalized-$\delta$-supplements. We attempt to investigate some properties of cofinitely weak generalized $\delta$-supplemented modules. We will prove for a module $M$ and a semi-$\delta$-hollow submodule $N$ of $M$ that, $M$ is cofinitely weak generalized $\delta$-supplemented if and only if $\frac{M}{N}$ is cofinitely weak generalized $\delta$-supplemented. Also we show that any $M$-generated module is cofinitely weak generalized $\delta$-supplemented module, where $M$ is cofinitely weak generalized $\delta$-supplemented. We obtain some other results about this kind of modules.https://as.yazd.ac.ir/article_1620_6e04b0ccf8f4d6c34d73900a02a8d152.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201A new lower bound for cohomological dimension2128162110.22034/as.2020.1621ENAlirezaNazariFaculty of Mathematical Sciences
Lorestan University
Khorram Abad
IranAsgharFarokhiFaculty of Mathematical Sciences, Lorestan University, Khorram Abad, Iran.Journal Article20190701Let $(R,\mathfrak{m})$ be a Noetherian local ring, $M$ a finitely generated $R$-module, and $\mathfrak{a}$ an ideal of $R$. We define the $\mathfrak{a}$-minimum dimension $d(\mathfrak{a},M)$ of $M$ by $$d(\mathfrak{a},M)=Min\{\dim \frac{R}{\mathfrak{p}+\mathfrak{a}}:\mathfrak{p}\in Assh_{R}(M)\}.$$ In this paper, we show that $cd(\mathfrak{a},M)\geq \dim M-d(\mathfrak{a},M)$ and we give some sufficient conditions and characterization for the equality to hold true.https://as.yazd.ac.ir/article_1621_42a77c099b9affb629ee988bbd224dbb.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201Finiteness of certain local cohomology modules2940168310.22034/as.2020.1683ENFatemehDehghani-ZadehDepartment of mathematics, Islamic Azad University Yazd Branch, Yazd, Iran.Journal Article20180427Cofiniteness of the generalized local cohomology modules <br />$H^{i}_{\mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with<br />respect to an ideal $\mathfrak{a}$ is studied for some $i^{,}s$ with<br />a specified property. Furthermore, Artinianness of<br />$H^{j}_{\mathfrak{b}_{0}}(H_{\mathfrak{a}}^{i}(M,N))$ is<br />investigated by using the above result, in certain graded situations, where $\mathfrak{b}_{0}$ is an ideal of $R_{0}$ and<br />$\mathfrak{a}=\mathfrak{a}_{0}+R_{+}$ such that<br />$\mathfrak{b}_{0}+\mathfrak{a}_{0}$ is an $\mathfrak{m}_{0}$-primary ideal.https://as.yazd.ac.ir/article_1683_92ccb62b9dfb36a39864bdff4e2f2d5e.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201On the Schur pair of groups4147168610.22034/as.2020.1686ENMahboubehAlizadeh SanatiDepartment of mathematics, Faculty of Sciences, Golestan University, Gorgan.0000-0001-6626-8059Journal Article20190505In this paper, it is shown that $ (\mathcal{V}, \mathfrak{X}) $ is a Schur pair if and only if the Baer-invariant of an $\mathfrak{X}$-group with respect to $ \mathcal{V}$ is an $\mathfrak{X}$-group. Also, it is proved that a locally $\mathfrak{X}$ class inherited the Schur pair property of , whenever $\mathfrak{X}$ is closed with respect to forming subgroup, images and extensions of its members. Subsequently, many interesting predicates about some generalizations of Schur's theorem and Schur multiplier of groups will be concluded.https://as.yazd.ac.ir/article_1686_354df22c5037c7fc7aaee99df8987e37.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201$H$-supplemented modules and singularity4957171710.22034/as.2020.1717ENAli RezaMoniri HamzekolaeeDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar0000-0002-2852-7870Journal Article20190829Let $M$ be a module over a ring $R$. We call $M$,$\delta$-$H$-supplemented provided for every submodule $N$ of $M$ there is a direct summand $D$ of $M$ such that $M=N+X$ if and only if $M=D+X$ for every submodule $X$ of $M$ with $M/X$ singular. We prove that $M$ is $\delta$-$H$-supplemented if and only if for every submodule $N$ of $M$ there exists a direct summand $D$ of $M$ such that $(N+D)/N\ll_{\delta} M/N$ and $(N+D)/D\ll_{\delta} M/D$.https://as.yazd.ac.ir/article_1717_57059068e17920865933936d97025ae6.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201On some designs constructed from the groups $PSL_{2}(q)$, $q=53,61,64$5967171810.22034/as.2020.1718ENRezaKahkeshaniDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran0000-0001-8044-803XJournal Article20190725In this paper, we use the primitive permutation representations of the simple groups $PSL_2(53)$, $PSL_2(61)$ and $PSL_2(64)$ and construct 1-designs by the Key-Moori Method 1.<br />It is shown that the groups $PSL_2(53)$, $PSL_2(53)\text{:}2$, $PSL_2(61)$, $PSL_2(61)\text{:}2$, $PSL_2(64)$, $PSL_2(64)\text{:}2$, $PSL_2(64)\text{:}3$ and $PSL_2(64)\text{:}6$ appear as the full automorphism groups of these obtained designs.https://as.yazd.ac.ir/article_1718_0827e60cd6a3b0bb0abbfe07f2e9e2a5.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201Commutativity degree and non-commuting graph in finite groups and Mofang Loops and their relationships6982171910.22034/as.2020.1719ENElhamehRezaieDepartment of Mathematics, Science and Research Branch, Islamic Azad University, P.O. Box 14515-1775, Tehran, Iran.KarimAhmadidelirDepartment of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.0000-0001-7244-8216AbolfazlTehranianDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranJournal Article20190401Terms like commutativity degree, non-commuting graph and isoclinism are far well-known for much of the group theorists nowadays. There are so many papers about each of these concepts and also about their relationships in finite groups. Also, there are some recent researches about generalizing these notions in finite rings and their connexions.<br />The concepts of commutativity degree and non-commuting graph are also extended to non-associative structures such as Moufang loops and some part of the known results in group theory in these contexts have been expanded to them.<br />In this paper, we are going to generalize the notion of isoclinism in finite Moufang loops and then study the relationships between these three concepts. Among other results, we prove that two isoclinic finite Moufang loops have the same commutativity degree and if they have the same sizes of centers and commutants then they have isomorphic non-commuting graphs. Also, the converses of these results have been investigated.<br />Furthermore, it has been proved that a finite simple group can be characterized by its non-commuting graph. We will prove the same is true for a finite simple Moufang loop by imposing one additional hypothesis, namely, the isoclinism of the regarding loops.https://as.yazd.ac.ir/article_1719_1cdaa8e90e8448061422b7fdbb038e03.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201The strongly annihilating-submodule graph of a module8399172010.22034/as.2020.1720ENAhadollahFarzi-SafarabadiDepartment of Mathematics, Lorestan University, Khorramabad, IranRezaBeyranvandDepartment of Mathematics,
Lorestan university,
Khorramabad, IranJournal Article20181215In this paper, we define the notion of strongly annihilating-submodule graph of modules. This graph is a straightforward common generalization of the annihilating-submodule graph and the annihilating-ideal graph. In addition to providing the properties of this graph in general, we investigate the behavior of the graph when modules are reduced or divisible.https://as.yazd.ac.ir/article_1720_735397588383f4bf6ff90d78d9c96b4b.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201Some categorical structures of generalized topologies in terms of monotone operators101115173410.22034/as.2020.1734ENTahereMohammadi KhorsandDepartment of Mathematics, University of Hormozgan, Bandarabbas, IranGhasemMirhosseinkhaniDepartment of mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran.Journal Article20191117In this paper, we give some generalized categories of topological spaces in terms of monotone operators and investigate some categorical properties of them. In particular, we present some equivalent categories of generalized topological spaces in terms of closure and interior operators. Also, we study the properties of some classes of morphisms as final, initial, closed and open morphisms in these categories.https://as.yazd.ac.ir/article_1734_6e84dc2f50b03ed83aff7997213ab0f1.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201Convex, balanced and absorbing subsets of hypervector spaces117125173510.22034/as.2020.1735ENElhamZangiabadiDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, P. O. Box 7713936417, Rafsanjan, IranZohrehNazariDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, P. O. Box 7713936417, Rafsanjan, IranJournal Article20180628In this paper, we define convex, balanced and absorbing subsets of a hypervector space $V$ over a field $K$, where $K$ is considered $\mathbb{R}$ or $\mathbb{C}$ and give some examples of them. We prove that every subspace of a hypervector space is a convex and balanced subset. Also, for every regular equivalence relation $\rho$ on a hypervector space $V$, we show that if $A$ is a convex, balanced or an absorbing subset of $V$, then $A/\rho$ is respectively a convex, balanced or an absorbing subset of a hypervector space $V/\rho$.https://as.yazd.ac.ir/article_1735_97f0c335d981a14177b59c2ae16bbf39.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617120200201On medial filters of BE-algebras127141173610.22034/as.2020.1736ENAkbarRezaeiDepartment of Mathemtics, Payame Noor University, P.O.Box. 19395-3697, Tehran, Iran.0000-0002-6003-3993AkefeRadfarDepartment of Mathematics,
Payame Noor University, P.O.Box. 19395-3697, Tehran, Iran.0000-0002-2345-4609AmirPourabdollahSchool of Computer Science,
The University of Nottingham, Nottingham NG8 1BB, UK0000-0001-7737-1393Journal Article20190912In this paper, the notion of a medial filter in a BE-algebra is defined, and the theory of filters in BE-algebras is developed. These filters are very important for the study of congruence relations in BE-algebras. <br />Moreover, the relationships between implicative filters, medial filters and normal filters are investigated.https://as.yazd.ac.ir/article_1736_6e053db6bc1477c1eb5a3576dc46b3a3.pdf