On the local-global principles for the $CD_{ < n}$ of local cohomology modules
Marziyeh
Hatamkhani
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran.
author
Hajar
Roshan-Shekalgourabi
Department of Basic Sciences, Arak University of Technology, P. O. Box 38135-1177, Arak, Iran.
author
text
article
2021
eng
The concept of Faltings' local-global principle for $CD_{ < n}$ of local cohomology modules over a Noetherian ring $R$ is introduced, and it is shown that this principle holds at levels 1, 2 over local rings. We also establish the same principle at all levels over an arbitrary Noetherian local ring of dimension not exceeding 3. These generalize the main results of Brodmann et al. in [9].
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
1
15
https://as.yazd.ac.ir/article_1970_886b32f5c728696aad4df960ca668ec3.pdf
dx.doi.org/10.22034/as.2021.1969
Construction of new gyrogroups and the structure of their subgyrogroups
Soheila
Mahdavi
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
Mohammad
Salahshour
Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, I. R. Iran
author
text
article
2021
eng
Suppose that $G$ is a groupoid with binary operation $\otimes$. The pair $(G,\otimes)$ is said to be a gyrogroup if the operation $\otimes$ has a left identity, each element $a \in G$ has a left inverse and the left gyroassociative law and the left loop property are satisfied in $G$. In this paper, a method for constructing new gyrogroups from old ones is presented and the structure of subgyrogroups of these gyrogroups are also given. As a consequence of this work, five $2-$gyrogroups of order $2^n$, $n\geq 3$, are presented. Some open questions are also proposed.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
17
30
https://as.yazd.ac.ir/article_1971_7e601c6ea84946f4cc0d5bceeb7505c1.pdf
dx.doi.org/10.22034/as.2021.1971
The $(p,q,r)$-generations of the symplectic group $Sp(6,2)$
Ayoub
Basheer
School of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga 0727, South Africa.
author
Malebogo
Motalane
School of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga 0727, South Africa.
author
Thekiso
Seretlo
School of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga 0727, South Africa.
author
text
article
2021
eng
A finite group $G$ is called \textit{$(l,m, n)$-generated}, if it is a quotient group of the triangle group $T(l,m, n) = \left<x, y, z|x^{l} = y^{m} = z^{n} = xyz = 1\right>.$ In 29, Moori posed the question of finding all the $(p,q,r)$ triples, where $p,\ q$ and $r$ are prime numbers, such that a non-abelian finite simple group $G$ is a $(p,q,r)$-generated. In this paper we establish all the $(p,q,r)$-generations of the symplectic group $Sp(6,2).$ GAP 20 and the Atlas of finite group representations 33 are used in our computations.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
31
49
https://as.yazd.ac.ir/article_1975_71c4190f69964e4c878ac7ca9e23a65b.pdf
dx.doi.org/10.22034/as.2021.1975
On the NSE characterization of certain finite simple groups
Sakineh
Rahbariyan
Department of Mathematics, Faculty of Sciences, Arak University, Arak, Iran.
author
Azizollah
Azad
Department of Mathematics, Faculty of Sciences, Arak University, Arak, Iran.
author
text
article
2021
eng
For a group $G$, $\pi_e(G)$ and $s_m(G)$ are denoted the set of orders of elements and the number of elements of order $m$ in $G$, respectively. Let ${\rm nse}(G)=\{s_m(G) \ | \ m\in \pi_e(G)\}$. An arbitrary finite group $M$ is NSE characterization if, for every group $G$, the equality ${\rm nse}(G)={\rm nse}(M)$ implies that $G\cong M$. In this paper, we are going to show that the non-Abelian finite simple groups $A_9$, $A_{10}$, $A_{12}$, $U_4(3)$, $U_5(2)$, $U_6(2)$, $S_6(2)$, $O_8^+(2)$ and $HS$ are characterizable by NSE.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
51
65
https://as.yazd.ac.ir/article_1977_92547878e500a63cd421fe548f225699.pdf
dx.doi.org/10.22034/as.2021.1977
Spectral aspects of commuting conjugacy class graph of finite groups
Parthajit
Bhowal
Department of Mathematical Sciences, Tezpur university, Napaam Assam, India.
author
Rajat
Nath
Department of Mathematical Sciences, Tezpur University, Sonitpur, India
author
text
article
2021
eng
The commuting conjugacy class graph of a non-abelian group $G$, denoted by $\mathcal{CCC}(G)$, is a simple undirected graph whose vertex set is the set of conjugacy classes of the non-central elements of $G$ and two distinct vertices $x^G$ and $y^G$ are adjacent if there exists some elements $x' \in x^G$ and $y' \in y^G$ such that $x'y' = y'x'$. In this paper we compute various spectra and energies of commuting conjugacy class graph of the groups $D_{2n}, Q_{4m}, U_{(n, m)}, V_{8n}$ and $SD_{8n}$. Our computation shows that $\mathcal{CCC}(G)$ is super integral for these groups. We compare various energies and as a consequence it is observed that $\mathcal{CCC}(G)$ satisfy E-LE Conjecture of Gutman et al. We also provide negative answer to a question posed by Dutta et al. comparing Laplacian and Signless Laplacian energy. Finally, we conclude this paper by characterizing the above mentioned groups $G$ such that $\mathcal{CCC}(G)$ is hyperenergetic, L-hyperenergetic or Q-hyperenergetic.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
67
118
https://as.yazd.ac.ir/article_1979_d3b7e9534acf0d7b8751c583f390e093.pdf
dx.doi.org/10.22034/as.2021.1979
Some remarks on goursat lemma
Brice Rene
Amougou Mbarga
Department of mathematics, University of Yaounde 1, Yaounde, Cameroon.
author
text
article
2021
eng
In this article,we give a characterization of containment of subgroups in a direct product $A\times B\times C$. Other potential generalizations are investigated and applications characterizing different types of groups and modules are given. Most of applications are simple while somewhat deeper applications occur in the case of cyclic modules.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
119
129
https://as.yazd.ac.ir/article_2022_28a17764e8bccb18b75f6e002ee69f82.pdf
dx.doi.org/10.22034/as.2021.2022
An algorithm for finding minimal generating sets of finite groups
Tanakorn
Udomworarat
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
author
Teerapong
Suksumran
Department of Mathematics, Faculty of Science, Chiang Mai University,
Chiang Mai 50200, Thailand
author
text
article
2021
eng
In this article, we study connections between components of the Cayley graph $\mathrm{Cay}(G,A)$, where $A$ is an arbitrary subset of a group $G$, and cosets of the subgroup of $G$ generated by $A$. In particular, we show how to construct generating sets of $G$ if $\mathrm{Cay}(G,A)$ has finitely many components. Furthermore, we provide an algorithm for finding minimal generating sets of finite groups using their Cayley graphs.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
131
143
https://as.yazd.ac.ir/article_2029_1faa89d54035328fbec3e75bcf9036ae.pdf
dx.doi.org/10.22034/as.2021.2029
On pseudo-contractibility of certain algebras related to a discrete semigroup
Amir
Sahami
Department of Mathematics Faculty of Basic Sciences Ilam University P.O. Box 69315-
516 Ilam, Iran.
author
Mehdi
Rostami
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran,
Iran.
author
Shahab
Kalantari
Department of Basic Science, Babol Noshirvani University of Technology, Shariati Avenue, Babol 47148-71167, Iran.
author
text
article
2021
eng
In this paper, we introduce a notion of ultra central approximate identity for Banach algebras which is a generalization of the bounded approximate identity and the central approximate identity. Using this concept we study pseudo-contractibility of some matrix algebras among $\ell^1$-Munn algebras. As an application, for the Brandt semigroup $S=M^{0}(G,I)$ over a non-empty set $I$, we show that $\ell^{1}(S)$ has an ultra central approximate identity if and only if $I$ is finite. Also we show that the notion of pseudo-contractibility and contractibility are the same on $\ell^{1}(S)^{**}$, where $S$ is the Brandt semigroup.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
145
155
https://as.yazd.ac.ir/article_2050_e2e1042b2414d649559951430bcf9731.pdf
dx.doi.org/10.22034/as.2021.2050
Characterizations of ordered semihypergroups via (M, N)-int-soft bi-hyperideals
Muhammad
Farooq
Government Higher Secondary School, Mohib Banda, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.
author
Asghar
Khan
Department of mathematics, Abdul Wali Khan University, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.
author
Muhammad
Izhar
Department of mathematics, Government Degree College Garhi Kapura, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.
author
text
article
2021
eng
The aim of this article is to study ordered semihypergroups in the framework of $( {M, N})$-int-soft bi-hyperideals. In this paper, we introduce the notion of $(M, N) $-int-soft bi-hyperideals\ of ordered semihypergroups. Some properties of $({M, N})$-int-soft bi-hyperideals in ordered semihypergroups are provided. We show that every int-soft bi-hyperideal is an $({M, N})$-int-soft bi-hyperideals of $S$ over $U$ but the converse is not true which is shown with help of an example. We characterize left $({M, N})$ simple and completely regular ordered semihypergroups by means of $({M, N})$-int-soft bi-hyperideals.The aim of this article is to study ordered semihypergroups in the framework of $\left( {M, N}\right)$-int-soft bi-hyperideals. In this paper, we introduce the notion of $\left( {M, N}\right)$-int-soft bi-hyperideals of ordered semihypergroups. Some properties of $\left( {M, N}\right)$-int-soft bi-hyperideals in ordered semihypergroups are provided. We show that every int-soft bi-hyperideal is an $\left( {M, N}\right)$-int-soft bi-hyperideals of $S$ over $U$ but the converse is not true which is shown with help of an example. We characterize left $\left( \text{resp. right}\right)$ simple and completely regular ordered semihypergroups by means of $\left( {M, N}\right)$-int-soft bi-hyperideals.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
157
175
https://as.yazd.ac.ir/article_2051_a7691ccf69442c210041d7e65d164ea0.pdf
dx.doi.org/10.22034/as.2021.2051
Homoderivations and semigroup ideals in $3$-prime near-rings
Samir
Mouhssine
University Sidi Mohammed Ben Abdellah,
Polydisciplinary Faculty, Department of Mathematics,
Physics and Computer Science, LSI, Taza; Morocco.
author
Abdelkarim
Boua
University Sidi Mohammed Ben Abdellah, Polydisciplinary Faculty, Department of Mathematics,
Physics and Computer Science, LSI, Taza; Morocco.
author
text
article
2021
eng
This paper studies homoderivations satisfying certain conditions on semigroup ideals of near-rings. In addition, we include some examples of the necessity of the hypotheses used in our results.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
177
194
https://as.yazd.ac.ir/article_2110_f9680f36382e46fed705244ba6b17c04.pdf
dx.doi.org/10.22034/as.2021.2110
On graded $J_{gr}$-classical prime submodules
khaldoun
Al-Zoubi
Department of Mathematics and
Statistics, Faculty of Science and Arts Jordan University of Science and Technology, P.O.Box
3030, Irbid 22110, Jordan.
author
Shatha
Alghueiri
Department of Mathematics and
Statistics, Faculty of Science and Arts Jordan University of Science and Technology, P.O.Box
3030, Irbid 22110, Jordan.
author
text
article
2021
eng
Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with identity 1 and $M$ a graded $R$-module. A proper graded submodule $C$ of $M$ is called a graded classical prime submodule if whenever $r,s\in h(R)$ and $m\in h(M)$ with $rsm\in C$, then either $rm\in C$ or $sm\in C$. In this paper, we introduce the concept of graded $J_{gr}$-classical prime submodule as a new generalization of graded classical submodule and we give some results concerning such graded modules. We say that a proper graded submodule $N$ of $M$ is \textit{a graded }$J_{gr}$\textit{-classical prime submodule of \ }$M$ if whenever $rsm\in N$ where $r,s\in h(R)$ and $m\in h(M)$, then either $rm\in N+J_{gr}(M)$ or $sm\in N+J_{gr}(M)$, where $J_{gr}(M)$ is the graded Jacobson radical.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
195
201
https://as.yazd.ac.ir/article_2121_5bd6ab9b64e4a6a1a3c24c741a28c88a.pdf
dx.doi.org/10.22034/as.2021.2121
2-Domination in vague graphs
Sadegh
Banitalebi
Department of Knowledge and Cognitive Intelligence, Imam Hossein University, Tehran, Iran.
author
Rajab Ali
Borzooei
Department of Mathematics, Shahid Beheshti University, Tehran, Iran.
author
Elahe
Mohamadzadeh
Department of Mathematics, Faculty of Science, Payam Noor University, Tehran, Iran.
author
text
article
2021
eng
A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the notions of (perfect-total) 2-dominating set and (perfect-total) 2-domination numbers on vague graphs are introduced and some properties are investigated. Especially, it is proven that in any strong vague graph on a Petersen graph, any minimal 2-dominating set is a minimal perfect 2-dominating set and minimal dominating set. Then, the concepts of (total) 2-cobondage set and (total) 2-cobondage number in vague graphs are expressed and related results obtained. Finally, an application related to Fire Stations and Emergency Medical centers is provided.
Algebraic Structures and Their Applications
Yazd University
2382-9761
8
v.
2
no.
2021
203
222
https://as.yazd.ac.ir/article_2164_344def5b5d8b2e369fe87ce289c94d72.pdf
dx.doi.org/10.22034/as.2021.2164