Yazd UniversityAlgebraic Structures and Their Applications2382-97617220200401The secondary radicals of submodules113178610.29252/as.2020.1786ENHabibollahAnsari-ToroghyDepartment of pure Mathematics , Faculty of mathematical Sciences,
University of Guilan, Rasht, IranFaranakFarshadifarDepartment of Mathematics, Farhangian University, Tehran, IranFaridehMahboobi-AbkenarDepartment of pure Mathematics, Faculty of mathematical Sciences, University of Guilan, P. O. Box 41335-19141, Rasht, IranJournal Article20190920Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper, we will introduce the secondary radical of a submodule $N$ of $M$ as the sum of all secondary submodules of $M$ contained in $N$, denoted by $sec^*(N)$, and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual of primary radicals of submodules of $M$.http://as.yazd.ac.ir/article_1786_3aeace19649ddcff3fd467d347b417d2.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401On graded hyperrings and graded hypermodules1528179110.29252/as.2020.1791ENFarkhondeFarzalipourDepartment of Mathematics, Payame Noor University (PNU),
P.O.BOX 19395-3697 Tehran, Iran,PeymanGhiasvandDepartment of Mathematics, Payame Noor University (PNU),
P.O.BOX 19395-3697 Tehran, Iran,0000-0003-4084-7057Journal Article20180626Let $G$ be a monoid with identity $e$. In this paper, first we introduce the notions of $G$-graded hyperrings, graded hyperideals and graded hyperfields in the sense of Krasner hyperring $R$. Also, we define the notion of a greded $R$-hypermodules and some examples are presented. Then we investigate graded maximal, graded prime and graded primary hyperideals of a graded hyperring $R$. Finally, we study graded maximal, graded prime and graded primary subhypermodules of a graded $R$-hypermodule $M$ and some interesting results on these concepts are given.http://as.yazd.ac.ir/article_1791_1318b56c185ac726cdb9e35f0595c775.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401Cayley graph associated to a semihypergroup2949179210.29252/as.2020.1792ENKhadijehShamsiDepartment of Mathematics, Payamenoor University, P.O. Box 19395-4697, Tehran, IranRezaAmeriDepartment of mathematics, University of Tehran, Tehran, Iran.SaeedMirvakiliDepartment of mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, IranJournal Article20190610The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first we associate a Cayley graph to every semihypergroup and then we study the<br />properties of this graph, such as Hamiltonian cycles in this graph. Also, by some of examples we will illustrate the properties and behavior of these Cayley graphs, in particulars we show that the properties of a Cayley graph associated to a semihypergroup is completely different with respect to the Cayley graph associated to a semigroup(group). Also, we briefly discuss on category of Cayley graphs associated to semihypergroups and construct a functor from this category to the category of digraphs. Finally, we give an application the Cayley graph of a hypergroupoid to a social network.http://as.yazd.ac.ir/article_1792_4ebcacff5c8b497457c16e0a6a81eb13.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401An upper bound on the distinguishing index of graphs with minimum degree at least two5162179310.29252/as.2020.1793ENSaeidAlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran0000-0002-1801-203XSamanehSoltaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, IranJournal Article20191203The distinguishing index of a simple graph $G$, denoted by $D'(G)$, is the least number of labels in an edge labeling of $G$ not preserved by any non-trivial automorphism. We prove that for a connected graph $G$ with maximum degree $Delta$, if the minimum degree is at least two, then $ D'(G)leq lceil sqrt{Delta }rceil +1$. We also present graphs $G$ for which $D'(G)leq lceil sqrt{Delta (G)}rceil$.http://as.yazd.ac.ir/article_1793_05c3edbe547f4e7061cabdae9dc22d1b.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401Neutrosophic quadruple BCI-commutative ideals6377179410.29252/as.2020.1794ENG.R.RezaeiDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.R.A.BorzoueiDepartment of Mathematics, Shahid Beheshti University, Tehran, IranYoung BaeJunDepartment of Mathematics Education, Gyeong sang National university, Chinju, Korea0000-0002-0181-8969Journal Article20190527The notion of a neutrosophic quadruple BCI-commutative ideal in a neutrosophic quadruple BCI-algebra is introduced, and several properties are investigated. Relations between a neutrosophic quadruple ideal and a neutrosophic quadruple BCI-commutative ideal are discussed, and conditions for the neutrosophic quadruple ideal to be a neutrosophic quadruple BCI-commutative ideal are given. Conditions for the neutrosophic quadruple set to be a neutrosophic quadruple BCI-commutative ideal are provided, and the extension property of a neutrosophic quadruple BCI-commutative ideal is considered.http://as.yazd.ac.ir/article_1794_0b0e15de4485b29fd8c2ad1c31796c89.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401A class of well-covered and vertex decomposable graphs arising from rings7991179510.29252/as.2020.1795ENMortezaVafaeiDepartment of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran.AbolfazlTehranianDepartment of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran.RezaNikandishDepartment of Mathematics,
Jundi-Shapur University of Technology, Dezful, Iran.Journal Article20180924Let $ mathbb {Z}_{n} $ be the ring of integers modulo $ n $. The unitary Cayley graph of $ mathbb {Z}_{n} $ is defined as the graph $ G( mathbb {Z}_{n} ) $ with the vertex set $ mathbb {Z}_{n} $ and two distinct vertices $a,b$ are adjacent if and only if $a-bin Uleft( mathbb {Z}_{n}right)$, where $ Uleft( mathbb {Z}_{n}right) $ is the set of units of $ mathbb {Z}_{n} $. Let $Gamma ( mathbb {Z}_{n} ) $ be the complement of $ G( mathbb {Z}_{n} ) $. In this paper, we determine the independence number of $ Gamma ( mathbb {Z}_{n} ) $. Also it is proved that $ Gamma ( mathbb {Z}_{n} ) $ is well-covered. Among other things, we provide condition under which $ Gamma ( mathbb {Z}_{n} ) $ is vertex decomposable.http://as.yazd.ac.ir/article_1795_69319c6fcdc62a4d6775d571b211f51a.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401Free ideals and real ideals of the ring of frame maps from $mathcal P(mathbb R)$ to a frame93113179810.29252/as.2020.1798ENAliEstajiFaculty of Mathematics and Computer Sciences,
Hakim Sabzevari University,
Postal Code 9617976487,
Sabzevar,
IranAhmadMahmoudi DarghadamFaculty of Mathematics and Computer Sciences,
Hakim Sabzevari University,
Sabzevar,
Iran.0000-0001-9416-6041Journal Article20200323Let $mathcal F_{mathcal P}( L)$ ($mathcal F_{mathcal P}^{*}( L)$) be the $f$-rings of all (bounded) frame maps from $mathcal P(mathbb R)$ to a frame $L$. $mathcal F_{{mathcal P}_{infty}}( L)$ is the family of all $fin mathcal F_{mathcal P}( L)$ such that ${uparrow}f(-frac 1n, frac 1n)$ is compact for any $ninmathbb N$ and the subring $mathcal F_{{mathcal P}_{K}}( L)$ is the family of all $fin mathcal F_{mathcal P}( L)$ such that ${{,mathrm{coz},}}(f)$ is compact. We introduce and study the concept of real ideals in $mathcal F_{mathcal P}( L)$ and $mathcal F_{mathcal P}^*( L)$. We show that every maximal ideal of $mathcal F_{mathcal P}^{*}( L)$ is real, and also we study the relation between the conditions ``$L$ is compact" and ``every maximal ideal of $mathcal F_{mathcal P}(L)$ is real''. We prove that for every nonzero real Riesz map $varphi colon mathcal F_{mathcal P}( L)rightarrow mathbb R$, there is an element $p$ in $Sigma L$ such that $varphi=widetilde {p_{{{,mathrm{coz},}}}}$<br /> if $L$ is a zero-dimensional frame for which $B(L)$ is a sub-$sigma$-frame of $L$ and every maximal ideal of $mathcal F_{mathcal P}( L)$ is real. We show that $mathcal F_{{mathcal P}_{infty}}(L)$ is equal to the intersection of all free maximal ideals of $ mathcal F_{mathcal P}^{*}(L) $ if $B(L)$ is a sub-$sigma$-frame of a zero-dimensional frame $L$ and also, $mathcal F_{{mathcal P}_{K}}(L)$ is equal to the intersection of all free ideals $mathcal F_{mathcal P}( L)$ (resp., $mathcal F_{mathcal P}^*( L)$) if $L$ is a zero-dimensional frame. Also, we study free ideals and fixed ideals of $mathcal F_{{mathcal P}_{infty}}( L)$ and $mathcal F_{{mathcal P}_{K}}( L)$.http://as.yazd.ac.ir/article_1798_92d5328919dc23bb02ef57cb01f42e71.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401Topics in topological MI-groups115134180110.29252/as.2020.1801ENHosainBagheriDepartment of Mathematics, Yazd University, Yazd, Iran.Seyed Mohamad SadeghModarres MosadeghDepartment of mathematics,
Yazd University, Yazd, IranJournal Article20200311A many identities group (MI-group, for short) is an algebraic structure which is generalized a monoid with cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In other words, an MI-group is an algebraic structure generalizing the group concept, except most of the elements have no inverse element. The concept of a topological MI-group, as a preliminary study, in the paper '' Topological MI-group: Initial study'' was introduced by M. Holv capek and N. v Skorupov' a, and we have given a more comprehensive study of this concept in our two recent papers. This article is a continuation of the effort to develop the theory of topological MI-groups and is focused on the study of separation axioms and the isomorphism theorems for topological MI-groups. Moreover, some conditions under which a MI-subgroup is closed will be investigated, and finally, the existence of nonnegative invariant measures on the locally compact MI-groups are introduced.http://as.yazd.ac.ir/article_1801_fb3adbd7f0ede9468d416c6cb243119d.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401Commuting conjugacy class graphs of finite groups135145189010.29252/as.2020.1839ENM. A.SalahshourDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. IranA. R.AshrafiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. IranJournal Article20190101Suppose that $G$ is a finite non-abelian group. Define the graph $Gamma(G)$ with the non-central conjugacy classes of $G$ as vertex set and two distinct vertices $A$ and $B$ are adjacent if and only if there are $x in A$ and $y in B$ such that $xy = yx$. The graph $Gamma(G)$ is called the commuting conjugacy class graph of $G$ and introduced by Mohammadian et al. in [A. Mohammadian, A. Erfanian, M. Farrokhi D. G. and B. Wilkens, Triangle-free commuting conjugacy class graphs, {J. Group Theory} {19} (3) (2016) 1049--1061]. In this paper, the graph structure of the commuting conjugacy class graph of nilpotent groups of order $n$ are obtained in which $n$ is not divisible by $p^5$, for every prime factor $p$ of $n$.http://as.yazd.ac.ir/article_1890_9c925a92cf11412456ac7a69ccb37169.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401Normal ideals in pseudo-complemented almost distributive lattices147161189110.29252/as.2020.1891ENRafiNoorbhashsaDepartment of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh - 522 101, India.RavikumarBandaruDepartment of Mathematics, GITAM(Deemed to be University), Hyderabad Campus, Telangana - 502 329, IndiaMSrujanaDepartment of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh - 522 101, India.Journal Article20200427In this paper, we introduced the concepts of normlet and normal ideal in a pseudo-complemented almost distributive lattice and studied its properties. We have characterized normal ideals and established equivalent conditions for every ideal to become a normal ideal. Also, derived equivalent conditions for the set of all prime normal ideals of a pseudo-complemented ADL to become a Hausdorff space.http://as.yazd.ac.ir/article_1891_274ed3045060b600f2c799767e42d7b4.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401On generalizations of vector and Banach spaces by hyperstructres163177192110.29252/as.2020.1921ENSohrabOstadhadi DehkordiDepartment of mathematics, University of Hormozgan, Hormozgan, Bandar abbas, Iran.Kar PingShumInstitute of Mathematics,Yunnan University, Kunming, 650091, P.R. ChinaJournal Article20200206In this paper, we generalize the vector space by considering the group as a canonical $m$-ary hypergroup, the field as a Krasner $(m,n)$-hyperfield. Moreover, we define the $m$-ary hyper Banach spaces and investigate some of their related properties.http://as.yazd.ac.ir/article_1921_c99339a1db7273dfdd7d729fd2f8a8b5.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97617220200401Annihilators and attached primes of local cohomology modules with respect to a system of ideals179193195910.29252/as.2020.1959ENCam Thi HongBuiDepartment of Natural Science Education, Dong Nai University, Bien Hoa city, Dong Nai province, Vietnam.Journal Article20201119Let $Phi$ be a system of ideals of a commutative Noetherian ring, we study the annihilators and attached primes of local cohomology modules with respect to a system of ideals. We prove that if $M$ is a non-zero finitely generated $R$-module of finite dimension $d$ and $Phi$ is a system of ideals, then$$Att(H^d_Phi(M))={pin Ass Mmid cd(Phi,R/p)=d}.$$ Moreover, if the cohomology dimension of $M$ with respect to $Phi$ is $dim M-1,$ then $$Att(H^{dim M-1}_Phi(M))={pin Supp M mid cd(Phi,R/p)=dim M-1}.$$http://as.yazd.ac.ir/article_1959_9b5d18a0337b25e6a43e8740d26697ab.pdf