Yazd UniversityAlgebraic Structures and Their Applications2382-97618220210801On the local-global principles for the $CD_{ < n}$ of local cohomology modules115197010.29252/as.2021.1969ENMarziyehHatamkhaniDepartment of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran.HajarRoshan-ShekalgourabiDepartment of Basic Sciences, Arak University of Technology, P. O. Box 38135-1177, Arak, Iran.Journal Article20201010The 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].http://as.yazd.ac.ir/article_1970_e188dc6e3205a6a8c0619895ce5b9c1e.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801Construction of new gyrogroups and the structure of their subgyrogroups1730197110.29252/as.2020.1971ENSoheilaMahdaviDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. IranAli RezaAshrafiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran.0000-0002-2858-0663Mohammad AliSalahshourDepartment of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, I. R. Iran0000-0002-0816-4232Journal Article20200918Suppose 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.http://as.yazd.ac.ir/article_1971_57b542382bc883cae4f3bba305026d67.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801The $(p,q,r)$-generations of the symplectic group $Sp(6,2)$3149197510.29252/as.2021.1975ENAyoubBasheerSchool of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga 0727, South Africa.Malebogo JohnMotalaneSchool of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga 0727, South Africa.0000-0003-4484-4355Thekiso TrevorSeretloSchool of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga 0727, South Africa.Journal Article20200714A 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.http://as.yazd.ac.ir/article_1975_cc7b7f4360213202176c6b3746b0b84f.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801On the NSE characterization of certain finite simple groups5165197710.29252/as.2021.1977ENSakinehRahbariyanDepartment of Mathematics, Faculty of Sciences, Arak University, Arak, Iran.AzizollahAzadDepartment of Mathematics, Faculty of Sciences, Arak University, Arak, Iran.Journal Article20200724For 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.http://as.yazd.ac.ir/article_1977_c0ae6343e91657dad472eda248e56e1f.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801Spectral aspects of commuting conjugacy class graph of finite groups67118197910.29252/as.2021.1979ENParthajitBhowalDepartment of Mathematical Sciences, Tezpur university, Napaam Assam, India.0000-0002-8001-9953Rajat KantiNathDepartment of Mathematical Sciences, Tezpur University, Sonitpur, IndiaJournal Article20200826The 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.http://as.yazd.ac.ir/article_1979_f2959d9ff29815c1d5cd9c3a6fd7c0d8.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801Some remarks on goursat lemma119129202210.29252/as.2021.2022ENBrice ReneAmougou MbargaDepartment of mathematics, University of Yaounde 1, Yaounde, Cameroon.Journal Article20200322In 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.http://as.yazd.ac.ir/article_2022_076536985560d7b982ebb1c9e2e026cd.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801An algorithm for finding minimal generating sets of finite groups131143202910.29252/as.2021.2029ENTanakornUdomworaratDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandTeerapongSuksumranDepartment of Mathematics, Faculty of Science, Chiang Mai University,
Chiang Mai 50200, Thailand0000-0002-1239-5586Journal Article20201205In 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.http://as.yazd.ac.ir/article_2029_208f295efff578ef13aba0f7242de476.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801On pseudo-contractibility of certain algebras related to a discrete semigroup145155205010.29252/as.2021.2050ENAmirSahamiDepartment of Mathematics Faculty of Basic Sciences Ilam University P.O. Box 69315-
516 Ilam, Iran.0000-0003-0041-509XMehdiRostamiFaculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran,
Iran.0000-0002-8989-0286ShahabKalantariDepartment of Basic Science, Babol Noshirvani University of Technology, Shariati Avenue, Babol 47148-71167, Iran.0000-0002-4439-8773Journal Article20201203In 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.http://as.yazd.ac.ir/article_2050_8f5135d33d25c10d29b62b28d4087d92.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801Characterizations of ordered semihypergroups via (M, N)-int-soft bi-hyperideals157175205110.29252/as.2021.2051ENMuhammadFarooqGovernment Higher Secondary School, Mohib Banda, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.AsgharKhanDepartment of mathematics, Abdul Wali Khan University, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.0000-0002-6846-662XMuhammadIzharDepartment of mathematics, Government Degree College Garhi Kapura, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.0000-0002-8849-8506Journal Article20191011The 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.http://as.yazd.ac.ir/article_2051_a5e7fe0f41d3398a071d4a55ec16d641.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801Homoderivations and semigroup ideals in $3$-prime near-rings177194211010.29252/as.2021.2110ENSamirMouhssineUniversity Sidi Mohammed Ben Abdellah,
Polydisciplinary Faculty, Department of Mathematics,
Physics and Computer Science, LSI, Taza; Morocco.AbdelkarimBouaUniversity Sidi Mohammed Ben Abdellah, Polydisciplinary Faculty, Department of Mathematics,
Physics and Computer Science, LSI, Taza; Morocco.Journal Article20200416This 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.http://as.yazd.ac.ir/article_2110_d10c252b11bc7479ffede50c769fe4c9.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97618220210801On graded $J_{gr}$-classical prime submodules195201212110.29252/as.2021.2121ENKhaldounAl-ZoubiDepartment of Mathematics and
Statistics, Faculty of Science and Arts Jordan University of Science and Technology, P.O.Box
3030, Irbid 22110, Jordan.0000-0001-6082-4480ShathaAlghueiriDepartment of Mathematics and
Statistics, Faculty of Science and Arts Jordan University of Science and Technology, P.O.Box
3030, Irbid 22110, Jordan.Journal Article20210129Let $G$ 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.http://as.yazd.ac.ir/article_2121_c6e6fb76d5ff39db1be5491c9b5280c2.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976182202108012-Domination in vague graphs203222216410.29252/as.2021.2164ENSadeghBanitalebiDepartment of Knowledge and Cognitive Intelligence, Imam Hossein University, Tehran, Iran.Rajab AliBorzooeiDepartment of Mathematics, Shahid Beheshti University, Tehran, Iran.0000-0001-7538-7885ElaheMohamadzadehDepartment of Mathematics, Faculty of Science, Payam Noor University, Tehran, Iran.Journal Article20200906A 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.http://as.yazd.ac.ir/article_2164_ad264ce79db30e6e0fc580166d99009b.pdf