The secondary radicals of submodules
Habibollah
Ansari-Toroghy
Department of pure Mathematics , Faculty of mathematical Sciences,
University of Guilan, Rasht, Iran
author
Faranak
Farshadifar
Department of Mathematics, Farhangian University, Tehran, Iran
author
Farideh
Mahboobi-Abkenar
Department of pure Mathematics, Faculty of mathematical Sciences, University of Guilan, P. O. Box 41335-19141, Rasht, Iran
author
text
article
2020
eng
Let $R$ 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 $M$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
1
13
https://as.yazd.ac.ir/article_1786_ae582ddd64975ffedb22c5fc5d89f8bd.pdf
dx.doi.org/10.22034/as.2020.1786
On graded hyperrings and graded hypermodules
Farkhonde
Farzalipour
Department of Mathematics, Payame Noor University (PNU),
P.O.BOX 19395-3697 Tehran, Iran,
author
Peyman
Ghiasvand
Department of Mathematics, Payame Noor University (PNU),
P.O.BOX 19395-3697 Tehran, Iran,
author
text
article
2020
eng
Let $G$ 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
15
28
https://as.yazd.ac.ir/article_1791_66cc165ded8e1e129fc31e815f5f7ecc.pdf
dx.doi.org/10.22034/as.2020.1791
Cayley graph associated to a semihypergroup
Khadijeh
Shamsi
Department of Mathematics, Payamenoor University, P.O. Box 19395-4697, Tehran, Iran
author
Reza
Ameri
Department of mathematics, University of Tehran, Tehran, Iran.
author
Saeed
Mirvakili
Department of mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran
author
text
article
2020
eng
The 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 theproperties 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
29
49
https://as.yazd.ac.ir/article_1792_570c85d6d13126ca5a7106f57ebc5bb5.pdf
dx.doi.org/10.22034/as.2020.1792
An upper bound on the distinguishing index of graphs with minimum degree at least two
Saeid
Alikhani
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
author
Samaneh
Soltani
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
author
text
article
2020
eng
The 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 $D'(G)\leq \lceil \sqrt{\Delta (G)}\rceil$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
51
62
https://as.yazd.ac.ir/article_3321_50f427e6985c01c27892c545212fd5cf.pdf
dx.doi.org/10.22034/AS.2020.1793
Neutrosophic quadruple BCI-commutative ideals
Gholam Reza
Rezaei
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
author
Rajab Ali
Borzouei
Department of Mathematics, Shahid Beheshti University, Tehran, Iran
author
Young Bae
Jun
Department of Mathematics Education, Gyeong sang National university, Chinju, Korea
author
text
article
2020
eng
The 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
63
77
https://as.yazd.ac.ir/article_1794_40313fdf246f673560fe9557e4d76b07.pdf
dx.doi.org/10.22034/as.2020.1794
A class of well-covered and vertex decomposable graphs arising from rings
Morteza
Vafaei
Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran.
author
Abolfazl
Tehranian
Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran.
author
Reza
Nikandish
Department of Mathematics,
Jundi-Shapur University of Technology, Dezful, Iran.
author
text
article
2020
eng
Let $ \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 $a-b\in U\left( \mathbb {Z}_{n}\right)$, where $ U\left( \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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
79
91
https://as.yazd.ac.ir/article_1795_f71952315a588d52310b4d416fda5b8c.pdf
dx.doi.org/10.22034/as.2020.1795
Free ideals and real ideals of the ring of frame maps from $\mathcal P(\mathbb R)$ to a frame
Ali
Estaji
Faculty of Mathematics and Computer Sciences,
Hakim Sabzevari University,
Postal Code 9617976487,
Sabzevar,
Iran
author
Ahmad
Mahmoudi Darghadam
Faculty of Mathematics and Computer Sciences,
Hakim Sabzevari University,
Sabzevar,
Iran.
author
text
article
2020
eng
Let $\mathcal F_{\mathcal P}( L)$ ($\mathcal F_{\mathcal P}^{*}( L)$) 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 $f\in \mathcal F_{\mathcal P}( L)$ such that ${\uparrow}f(-\frac 1n, \frac 1n)$ is compact for any $n\in\mathbb N$ and the subring $\mathcal F_{{\mathcal P}_{K}}( L)$ is the family of all $f\in \mathcal F_{\mathcal P}( L)$ 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 $\varphi=\widetilde {p_{{{\,\mathrm{coz}\,}}}}$ 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 $\mathcal F_{{\mathcal P}_{K}}( L)$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
93
113
https://as.yazd.ac.ir/article_1798_c4382f8727b44d614f536b322fe32db9.pdf
dx.doi.org/10.22034/as.2020.1798
Topics in topological MI-groups
Hosain
Bagheri
Department of Mathematics, Yazd University, Yazd, Iran.
author
Seyed Mohamad Sadegh
Modarres Mosadegh
Department of mathematics,
Yazd University, Yazd, Iran
author
text
article
2020
eng
A 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. Hol\v 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
115
134
https://as.yazd.ac.ir/article_1801_8adc47ebe8095f06929a53153d6be438.pdf
dx.doi.org/10.22034/as.2020.1801
Commuting conjugacy class graphs of finite groups
Mohammad
Salahshour
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran
author
Ali
Ashrafi
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran
author
text
article
2020
eng
Suppose 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 $n$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
135
145
https://as.yazd.ac.ir/article_1890_0db2624b23cedc6e3c371ad6f6be3a22.pdf
dx.doi.org/10.22034/as.2020.1839
Normal ideals in pseudo-complemented almost distributive lattices
Rafi
Noorbhashsa
Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh - 522 101, India.
author
Ravikumar
Bandaru
Department of Mathematics, GITAM(Deemed to be University), Hyderabad Campus, Telangana - 502 329, India
author
M
Srujana
Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh - 522 101, India.
author
text
article
2020
eng
In 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
147
161
https://as.yazd.ac.ir/article_1891_81a716febbf66a8a2c924ac09f40f2c2.pdf
dx.doi.org/10.22034/as.2020.1891
On generalizations of vector and Banach spaces by hyperstructres
Sohrab
Ostadhadi dehkordi
Department of mathematics, University of Hormozgan, Hormozgan, Bandar abbas, Iran.
author
Kar Ping
Shum
Institute of Mathematics,Yunnan University, Kunming, 650091, P.R. China
author
text
article
2020
eng
In 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
163
177
https://as.yazd.ac.ir/article_1921_f4dde424f33ef6c6b6aa25fd9afddec7.pdf
dx.doi.org/10.22034/as.2020.1921
Annihilators and attached primes of local cohomology modules with respect to a system of ideals
Cam
Bui
Department of Natural Science Education, Dong Nai University, Bien Hoa city, Dong Nai province, Vietnam.
author
text
article
2020
eng
Let $\Phi$ 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$$Att(H^d_\Phi(M))=\{p\in Ass M\mid cd(\Phi,R/p)=d\}.$$ Moreover, if the cohomology dimension of $M$ with respect to $\Phi$ is $dim M-1,$ then $$Att(H^{dim M-1}_\Phi(M))=\{p\in Supp M \mid cd(\Phi,R/p)=\dim M-1\}.$$
Algebraic Structures and Their Applications
Yazd University
2382-9761
7
v.
2
no.
2020
179
193
https://as.yazd.ac.ir/article_1959_594da6a80612845967cb4bf64b2a6e90.pdf
dx.doi.org/10.22034/as.2020.1959