Yazd UniversityAlgebraic Structures and Their Applications2382-97619120220201Quaternary codes and a class of 2-designs invariant under the group $A_8$112225410.29252/as.2021.2254ENRezaKahkeshaniDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran0000-0001-8044-803XJournal Article20210523In this paper, we use the Key-Moori Method 1 and construct a quaternary code $mathcal{C}_8$ from a primitive representation of the group $PSL_2(9)$ of degree 15. We see that $mathcal{C}_8$ is a self-orthogonal even code with the automorphism group isomorphic to the alternating group $A_8$. It is shown that by taking the support of any codeword $omega$ of weight $l$ in $mathcal{C}_8$ or $mathcal{C}_8^bot$, and orbiting it under $A_8$, a 2-$(15,l,lambda)$ design invariant under the group $A_8$ is obtained, where $lambda=binom{l}{2}|omega^{A_8}|/binom{15}{2}$. A number of these designs have not been known before up to our best knowledge. The structure of the stabilizers $(A_8)_omega$ is determined and moreover, primitivity of $A_8$ on each design is examined.http://as.yazd.ac.ir/article_2254_be337043b2d263eddd1337c7cfc96718.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201Very true GE-algebras1330230210.29252/as.2021.2302ENYoung BaeJunDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea.0000-0002-0181-8969Ravi KumarBandaruDepartment of Mathematics, GITAM,
Hyderabad Campus, Telangana-502329, India.0000-0001-8661-7914Manzoor KaleemShaikDepartment of Mathematics, St. Joseph's Degree College, Kurnool-518004, Andhra Pradesh, IndiaJournal Article20210716The concept of very true GE-algebra using very true operator is introduced and its properties are studied to expand the scope of research of GE-algebras. The concepts of simple very true GE-algebra and very true GE-filter are introduced. The characterization of simple very true GE-algebra is discussed, and several properties on very true GE-filter are investigated. Using a very true GE-filter, the quotient very true GE-algebra is constructed, and the uniform and topological space are established.http://as.yazd.ac.ir/article_2302_89b6fa8d7f344127450c5be3b9d97917.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201An approach to extending modules via homomorphisms3139230410.29252/as.2021.2304ENTayyebehAmouzegarDepartment of Mathematics, Quchan University of Technology, P.O.Box 94771-67335, Quchan, IranJournal Article20210505The notion of $mathcal{K}$-extending modules was defined recently as a proper generalization of both extending modules and Rickart modules. Let $M$ be a right $R$-module and let $S=End_R(M)$. We recall that $M$ is a $mathcal{K}$-extending module if for every element $phiin S$, $Kerphi$ is essential in a direct summand of $M$. Since a direct sum of $mathcal{K}$-extending modules is not a $mathcal{K}$-extending module in general, an open question is to find necessary and sufficient conditions for such a direct sum to be $mathcal{K}$-extending. In this paper, we give an answer to this question. We show that if $M_i$ is $M_j$-injective for all $i, jin I ={1, 2, dots, n}$, then $bigoplus_{i=1}^n M_i$ is a $mathcal{K}$-extending module if and only if $M_i$ is $M_j$-$mathcal{K}$-extending for all $i, j in I$. Other results on $mathcal{K}$-extending modules and some of their applications are also included. http://as.yazd.ac.ir/article_2304_6a738686bf731dba08f13270d014659e.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201Weakly primary semi-ideals in posets4151231810.29252/as.2021.2318ENK.PorselviDepartment of Mathematics,
Karunya Institute of Technology and Sciences
Coimbatore - 641 114, India.http://orcid.org/000B.ElavarasanDepartment of Mathematics,
Karunya Institute of Technology and Sciences
Coimbatore - 641 114, India.http://orcid.org/000Journal Article20210523One of the main goals of science and engineering is to avail human beings cull the maximum propitious decisions. To make these decisions, we need to ken human being's predictions, feasible outcomes of various decisions, and since information is never absolutely precise and accurate, we need to withal information about the degree of certainty. All these types of information will lead to partial orders. A partially ordered set (or poset) theory deals with partial orders and plays a major role in real life. It has wide range of applications in various disciplines such as computer science, engineering, medical field, science, modeling spatial relationship in geographic information systems (GIS), physics and so on. In this paper, we mainly focus on weakly primary semi-ideal of a poset. We introduce the concepts of weakly primary semi-ideal and weakly $Q$-primary semi-ideal for some prime $Q$ of a poset $P$ and characterize weakly primary semi-ideals of $P$ in terms of prime and primary semi-ideals of $P.$ We provide a counter-example for the existence of weakly primary semi-ideal of $P$ which is not a primary semi-ideal of $P.$ We found an equivalent assertion of primary (respy., weakly primary) semi-ideal $r(K)$ for a semi-ideal $K$ of $P.$ Moreover, we introduce the notion of direct product of weakly primary semi-ideal of $P$ and describe its characteristics.http://as.yazd.ac.ir/article_2318_0446e0858e104950e8e217ecdcd603a1.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201Deductive systems of GE-algebras5367231910.29252/as.2021.2319ENYoung BaeJunDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea.0000-0002-0181-8969RavikumarBandaruDepartment of Mathematics, GITAM, Hyderabad Campus, Telangana-502329, India.0000-0001-8661-7914Journal Article20210817A new sub-structure called (vivid) deductive system is introduced and their properties are examined. Conditions for a subset to be a deductive system are provided. The notion of upper GE-set is also introduced, and an example to show that any upper GE-set may not be a deductive system are supplied. Conditions for an upper GE-set to be a deductive system are provided. An upper GE-set is used to consider conditions for a subset to be a deductive system. The characterization of deductive system is established, and relationship between deductive system and vivid deductive system are created. Conditions for a deductive system to be a vivid deductive system are given, and the extension property for vivid deductive system is constructed.http://as.yazd.ac.ir/article_2319_e4f10c82e21e3c6dfd33f5bd551a5648.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201A variation of $delta$-lifting and $delta$-supplemented modules with respect to an equivalence relation6980233410.29252/as.2021.2334ENEsraÖztürk SözenDepartment of mathematics, Faculty of science and arts, Sinop University, Sinop, Turkey.0000-0002-2632-2193Journal Article20210309In this paper we introduce Goldie$^{ast }$-$delta $-supplemented modules as follows. A module $M$ is called Goldie$^{ast }$-$delta $-supplemented (briefly, G$_{delta }^{ast }$-supplemented) if there exists a $delta $-supplement $T$ of $M$ for every submodule $A$ of $M$ such that $Abeta_{delta }^{ast }T$. We say that a module $M$ is called Goldie$^{ast }$-$delta $-lifting (briefly, G$_{delta }^{ast }$-lifting) if there exists a direct summand $D$ of $M$ for every submodule $A$ of $M$ such that $Abeta_{delta }^{ast }D$. Note that the last concept given in [4] as a $delta $-$H$-supplemented module. We present fundamental properties of these modules. We indicate that these modules lie between $delta $-lifting and $delta $-supplemented modules. Also we prove that our modules coincide with some variations of $delta $-supplemented modules for $delta $-semiperfect modules.http://as.yazd.ac.ir/article_2334_e7232555c0c9541db3000a11c65d5569.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201On the cofiniteness of local cohomology modules8192238210.29252/as.2021.2382ENHajarRoshan-ShekalgourabiDepartment of Basic Sciences, Arak University of Technology, P. O. Box 38135-1177, Arak, Iran.Journal Article20191116Let $R$ be a commutative Noetherian ring with identity, $I$ be an ideal of $R$ and $M$ be an $R$-module such that $Ext^j_R(R/I, M)$ is finitely generated for all $j$. We prove that if $dim H^i_I(M)leq 1$ for all $i$, then for any $i geq 0$ and for any submodule $N$ of $H^i_I(M)$ that is either $I$-cofinite or minimax, the $R$-module $H^i_I(M)/N$ is $I$-cofinite. This generalizes the main result of Bahmanpour and Naghipour [8, Theorem 2.6]. As a consequence, the Bass numbers and Betti numbers of $H^i_I (M)$ are finite for all $i geq 0$. Also, among other things, we show that if either $dim R/Ileq 2$ or $dim Mleq 2$, then for each finitely generated $R$-module $N$, the $R$-module $Ext^j_R (N, H^i_I(M))$ is $I$-weakly cofinite, for all $i geq 0$ and $jgeq 0$. This generalizes [1, Corollary 2.8].http://as.yazd.ac.ir/article_2382_1cd3538db1f8913c26fbd9eb739796ba.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201Genus of commuting conjugacy class graph of certain finite groups93108244410.29252/as.2021.2444ENRajat KantiNathDepartment of Mathematical Sciences, Tezpur University, Sonitpur, IndiaParthajitBhowalDepartment of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India.
Department of Mathematics, Cachar College, Silchar-788001, Assam, India.0000-0002-8001-9953Journal Article20210130For a non-abelian group $G$, its commuting conjugacy class graph $mathcal{CCC}(G)$ 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 the genus of $mathcal{CCC}(G)$ for six well-known classes of non-abelian two-generated groups (viz. $D_{2n}, SD_{8n}, Q_{4m}, V_{8n}, U_{(n, m)}$ and $G(p, m, n)$) and determine whether $mathcal{CCC}(G)$ for these groups are planar, toroidal, double-toroidal or triple-toroidal.http://as.yazd.ac.ir/article_2444_7cdd7d7776dcd4b6c54aaaba29da750d.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201Automata on genetic structure109119246810.29252/as.2021.2468ENMridulDuttaDepartment of Mathematics, Dudhnoi College, Dudhnoi-783124, Goalpara, Assam, India.0000-0002-8692-2078SanjoyKalitaDepartment of Mathematics, School of Fundamental and Applied Sciences, Assam Don Bosco University, Tepesia-782402, Kamrup, Assam India.0000-0002-9670-1578Helen K.SaikiaDepartment of Mathematics, University of Gauhati, Guwahati-781014, Assam India.0000-0003-1971-9472Journal Article20201016In this paper, the authors have represented the genetic structures in terms of automata. With the algebraic structure defined on the genetic code authors defined an automaton on those codons as $Sigma = (C_G, P, A_M, F, G)$ where $P$ is the set of the four bases $A, C, G, U$ as a set of alphabets or inputs, $C_G$ is the set of all 64 codons, obtained from the ordering of the elements of $P$, as the set of states, $A_M$ is the set of the 20 amino acids as the set of outputs that produce during the process. $F$ and $G$ are transition function and output function respectively. Authors observed that $M(Sigma) = (lbrace f_a : a in P rbrace, circ)$ defined on the automata $Sigma$ where $f_a(q) = F(q, a) = qa, q in C_G, a in P$ is a monoid called the syntactic monoid of $Sigma$, with $f_a circ f_b = f_{ba}$ $forall a, b in P$. Studying the structure defined in terms of automata it is also observed that the algebraic structure $(M(C_G), +, cdot)$ forms a Near-Ring with respect to the two operations $' + '$ and $'cdot '$ where $M(C_G) = lbrace f vert f : C_G rightarrow C_G rbrace$.http://as.yazd.ac.ir/article_2468_3bf36d5f9af1d7f55282a5090bc13c41.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201Some aspects of unitary addition Cayley graph of Eisensteinintegers modulo $textit{n}$121132246910.29252/as.2021.2469ENJoyRoyDepartment of mathematics. Assam Don Bosco University, Tepesia. Assam, India.KuntalaPatraDepartment of mathematics, Gauhati University, Guwahati, Assam, India.Journal Article20210513The unitary addition Cayley graph $G_n[omega]$ of Eisenstein integers modulo $n$ has the vertex set $mathbb{E}_n[omega]$, the set of Eisenstein integers modulo $n$. Any two vertices $x=a_1+omega b_1$, $y=a_2+omega b_2$ of $G_n[omega]$ are adjacent if and only if $gcd(N(x+y),n)=1$, where $N$ is the norm of any element of $mathbb{E}_n[omega]$ given by $N(a+omega b)=a^2+b^2-ab$. In this paper we obtain some basic graph invariants such as degree of the vertices, number of edges, diameter, girth, clique number and chromatic number of unitary addition Cayley graph of Eisenstein integers modulo $n$. This paper also focuses on determining the independence number of the above mentioned graph.<br /> http://as.yazd.ac.ir/article_2469_4f75592b1bbbbc2f9494ef58adb32a29.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201Some aspects of marginal automorphisms of a finite $p$-group133143253810.29252/as.2021.2538ENRasoulSoleimaniDepartment of Mathematics, Payame Noor University (PNU), 19395-3697, Tehran, Iran.Journal Article20200122Let $F$ be a free group, $mathcal{V}$ be a variety of groups defined by the set of laws $Vsubseteq F$ and $G$ be a finite $mathcal{V}$-nilpotent $p$-group. The automorphism $alpha$ of $G$ is said to be a marginal automorphism (with respect to $V$), if for all $xin G$, $x^{-1}x^{alpha}in V^{star}(G)$, where $V^{star}(G)$ denotes the marginal subgroup of $G$. An automorphism $alpha$ of $G$ is called an IA-automorphism if $x^{-1}x^{alpha}in G'$ for each $xin G$. An automorphism $alpha$ of $G$ is called a class preserving if for all $xin G$, there exists an element $g_xin G$ such that $x^{alpha}=g_x^{-1}xg_x$. Let $operatorname{Aut}^{V^{star}}(G)$, $operatorname{Aut}^{G'}(G)$ and $operatorname{Aut}_c(G)$ respectively, denote the group of all marginal automorphisms, IA-automorphisms and class preserving automorphisms of $G$. In this paper, first we give a necessary and sufficient condition on a finite $mathcal{V}$-nilpotent $p$-group $G$ such that each marginal automorphism of $G$ fixes the center of $G$ element-wise. Then we characterize all finite $mathcal{V}$-nilpotent $p$-groups $G$ such that $operatorname{Aut}^{V^{star}}(G)=operatorname{Aut}^{G'}(G)$. Finally, we obtain a necessary and sufficient condition for a finite $mathcal{V}$-nilpotent $p$-group $G$ such that $operatorname{Aut}^{V^{star}}(G)=operatorname{Aut}_c(G)$.http://as.yazd.ac.ir/article_2538_bd9a820be9f7620328cc3754a7ff8637.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619120220201$omega$-filters of distributive lattices145159255310.29252/as.2021.2553ENMukkamalaSambasiva RaoDepartment of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh-535005, India.0000-0002-1627-9603ChukkaVenkata RaoDepartment of Mathematics, Albert Einstein School of Physical Sciences, Assam University, Silchar, Assam-788011, India.Journal Article20210919The notion of $omega$-filters is introduced in distributive lattices and their properties are studied. A set of equivalent conditions is derived for every maximal filter of a distributive lattice to become an $omega$-filter which leads to a characterization of quasi-complemented lattices. Some sufficient conditions are derived for proper $D$-filters of a distributive lattice to become an $omega$-filter. Finally, $omega$-filters of a distributive lattice are characterized with the help of minimal prime $D$-filters.http://as.yazd.ac.ir/article_2553_7eb5dd066be8f0f49ac173710d428f90.pdf