Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101SOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP105130158310.22044/jas.2018.5917.1296ENS.VisweswaranDepartment of Mathematics, Saurashtra University P.O.Box 360 005, Rajkot, India.P.VadhelDepartment of Mathematics, Saurashtra University P.O.Box 360 005, Rajkot, India.Journal Article20170619Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the graph-theoretic properties of the complement of the intersection graph of subgroups of G.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101THE SPECTRAL DETERMINATION OF THE MULTICONE GRAPHS Kw ▽ C WITH RESPECT TO THEIR SIGNLESS LAPLACIAN SPECTRA131141158410.22044/jas.2018.5879.1292ENA.Zeydi AbdianDepartment of Mathematical Sciences, Lorestan University, Lorestan, Khoramabad,
Iran.Gh. H.Fath-TabarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University
of Kashan, Kashan 87317-53153, Iran.M.Rahmani MoghaddamDepartment of Mathematics, Bu-Ali Sina University, Hamadan, Iran.Journal Article20170616The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of<br /> a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless Laplacian spectrum.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING143154158510.22044/jas.2019.7405.1365ENH.DorbidiDepartment of Mathematics, Faculty of Science, University of Jiroft, P.O. Box
78671-61167, Jiroft, Iran.S.AlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran.Journal Article20180827In this paper we introduce and study a graph on the set of ideals of a<br /> commutative ring $R$. The vertices of this graph are non-trivial ideals of $R$ and<br /> two distinct ideals $I$ and $J$ are adjacent if and only $IJ=Icap J$. We<br /> obtain some properties of this graph and study its<br /> relation to the structure of $R$.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101P-CLOSURE IN PSEUDO BCI-ALGEBRAS155165158610.22044/jas.2019.6332.1315ENH.HarizaviDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Journal Article20171020In this paper, for any non-empty subset C of a pseudo<br /> BCI-algebra X, the concept of p-closure of C, denoted by C(pc), is<br /> introduced and some related properties are investigated. Applying<br /> this concept, a characterization of the minimal elements of X is<br /> given. It is proved that C(pc) is the least closed pseudo BCI-ideal of X<br /> containing C and K(X) for any ideal C of X. Finally, by using the<br /> concept of p-closure, a closure operator is introduced.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101A KIND OF F-INVERSE SPLIT MODULES167178158710.22044/jas.2019.7211.1353ENM.HosseinpourDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,
P.O. Box 47416-95447, Babolsar, Iran.A. R.Moniri HamzekolaeeDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,
P.O. Box 47416-95447, Babolsar, Iran.0000-0002-2852-7870Journal Article20180630Let M be a right module over a ring R. In this manuscript,<br /> we shall study on a special case of F-inverse split modules<br /> where F is a fully invariant submodule of M introduced in [12].<br /> We say M is Z<br /> 2(M)-inverse split provided f^(-1)(Z2(M)) is a direct<br /> summand of M for each endomorphism f of M. We prove that M<br /> is Z2(M)-inverse split if and only if M is a direct sum of Z2(M)<br /> and a Z2-torsionfree Rickart submodule. It is shown under some<br /> assumptions that the class of right perfect rings R for which every<br /> right R-module M is Z2(M)-inverse split (Z(M)-inverse split) is<br /> precisely that of right GV-rings.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION179187158810.22044/jas.2019.7367.1363ENM.Mohagheghy NezhadDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box
1159, Mashhad, Iran.F.RahbarniaDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box
1159, Mashhad, Iran.M.MirzavaziriDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad, Iran.R.GhanbariDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box
1159, Mashhad, Iran.Journal Article20180815The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$. In this case, $B$ is called a textit{metric basis} for $G$. The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$. <br /> Giving a characterization for those graphs whose metric dimensions are two, we enumerate the number of $n$ vertex metric two dimensional graphs with basic distance 1.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101COMPUTING THE EIGENVALUES OF CAYLEY GRAPHS OF ORDER p2q189203158910.22044/jas.2019.7034.1344ENM.GhorbaniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785-136, I. R. Iran.A.Seyyed-HadiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785-136, I. R. Iran.F.Nowroozi-LarkiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785-136, I. R. Iran.Journal Article20180602A graph is called symmetric if its full automorphism group acts transitively on the set of arcs. The Cayley graph $Gamma=Cay(G,S)$ on group $G$ is said to be normal symmetric if $N_A(R(G))=R(G)rtimes Aut(G,S)$ acts transitively on the set of arcs of $Gamma$. In this paper, we classify all connected tetravalent normal symmetric Cayley graphs of order $p^2q$ where $p>q$ are prime numbers.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101A GENERALIZATION OF PRIME HYPERIDEALS IN KRASNER HYPERRINGS205216159010.22044/jas.2019.6407.1318ENL.Kamali ArdekaniFaculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran.B.DavvazDepartment of Mathematics, Yazd University, Yazd, Iran.Journal Article20171107In this paper, we extend the notion of 2-absorbing ideal on rings to Krasner hyperrings. In fact, we give a characterization of new generalization of prime hyperideals in Krasner hyperrings by introducing 2-absorbing hyperideals. <br /> We present some illustrative examples. Also, we study fundamental properties of 2-absorbing hyperideals on Krasner hyperrings and investigate some related results.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101EQUALIZERS IN THE CATEGORIES FUZZ AND TOPFUZZ217226159110.22044/jas.2019.7254.1355ENGh.MirhosseinkhaniDepartment of Mathematics and Computer Sciences, Sirjan University of Technology,
Sirjan, Iran.N.NazariDepartment of Mathematics, University of Hormozgan, Bandarabbas, Iran.Journal Article20180710It is well known that the categories Fuzz of fuzzes and TopFuzz<br /> of topological fuzzes are both complete and cocomplete, and some categorical<br /> properties of them were introduced by many authors. In this paper, we introduce<br /> the structure of equalizers in these categories. In particular, we show that every<br /> regular monomorphism is an injective map, but monomorphisms need not be<br /> injective, in general.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101ON SEMICOVERING, SUBSEMICOVERING, AND SUBCOVERING MAPS227244159210.22044/jas.2019.6941.1367ENM.KowkabiDepartment of Mathematics, University of Gonabad, P.O. Box 57678-96919, Gonabad,
Iran.B.MashayekhiDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-
91775, Mashhad, Iran.H.TorabiDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-
91775, Mashhad, Iran.Journal Article20180910In this paper, by reviewing the concept of subcovering and semicovering maps, we extend the notion of subcovering map to subsemicovering map. We present some necessary or sufficient conditions for a local homeomorphism to be a subsemicovering map. Moreover, we investigate the relationship between these conditions by some examples. Finally, we give a necessary and<br /> sufficient condition for a subsemicovering map to be semicovering.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101ON LOCAL ANTIMAGIC CHROMATIC NUMBER OF GRAPHS245256159310.22044/jas.2019.7933.1391ENS.ShaebaniSchool of Mathematics and Computer Science, Damghan University, P.O. Box
36716-41167, Damghan, Iran.Journal Article20181231A {it local antimagic labeling} of a connected graph $G$ with at least three vertices, is a bijection $f:E(G) rightarrow {1,2,ldots , |E(G)|}$ such that for any two adjacent vertices $u$ and $v$ of $G$, the condition <br /> $omega _{f}(u) neq omega _{f}(v)$ holds; where $omega _{f}(u)=sum _{xin N(u)} f(xu)$. Assigning $omega _{f}(u)$ to $u$ for each vertex $u$ in $V(G)$, induces naturally a proper vertex coloring of $G$; and $|f|$ denotes the number of colors appearing in this proper vertex coloring. The {it local antimagic chromatic number} of $G$, denoted by $chi _{la}(G)$, is defined as the minimum of $|f|$, where $f$ ranges over all local antimagic labelings of $G$.<br /> In this paper, we explicitly construct an infinite class of connected graphs $G$ such that $chi _{la}(G)$ can be arbitrarily large while $chi _{la}(G vee bar{K_{2}})=3$, where $G vee bar{K_{2}}$ is the join graph of $G$ and the complement graph of $K_{2}$. The aforementioned fact leads us to an infinite class of counterexamples to a result of [Local antimagic vertex coloring of a graph, <em>Graphs and Combinatorics</em> <strong>33</strong>} (2017), 275-285].Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS257269159410.22044/jas.2019.8150.1399ENM.AbediEsfarayen University of Technology, Esfarayen, North Khorasan, Iran.0000-0002-8763-4510Journal Article20190228We study primary ideals of the ring $mathcal{R}L$ of real-valued continuous functions on a completely regular frame $L$. We observe that prime ideals and primary ideals coincide in a $P$-frame. It is shown that every primary ideal in $mathcal{R}L$ is contained in a unique maximal ideal, and an ideal $Q$ in $mathcal{R}L$ is primary if and only if $Q capmathcal{R}^*L$ is a primary ideal in $mathcal{R}^*L$. We show that every pseudo-prime (primary) ideal in $mathcal{R}L$ is either an essential ideal or a maximal ideal which is at the same time a minimal prime ideal. Finally, we prove that if $L$ is a connected frame, then the zero ideal in $mathcal{R}L$ is decomposable if and only if $L={bf2}$.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101A REDUCTION IN THE SEARCH SPACE OF QC-LDPC CODES WITH GIRTH 8271280159510.22044/jas.2019.8086.1397ENF.AmirzadeFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood,
Iran.M.AlishahiFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood,
Iran.M.R.Rafsanjani-SadeghiDepartment of Mathematics and Computer Science, Amirkabir University of Technology,
Tehran, Iran.Journal Article20190216In this paper, we define a structure to obtain exponent matrices of girth-8 QC-LDPC codes with column weight 3. Using the difference matrices introduced by Amirzade et al., we investigate necessary and sufficient conditions which result in a Tanner graph with girth 8. Our proposed method contributes to reduce the search space in recognizing the elements of an exponent matrix. In fact, in this method we only search to obtain one row of an exponent matrix. The other rows are multiplications of that row.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101FILTER REGULAR SEQUENCES AND LOCAL COHOMOLOGY MODULES281290159610.22044/jas.2019.7493.1370ENJ.AzamiDepartment of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.Journal Article20180926Let R be a commutative Noetherian ring. In this paper we consider some relations between filter regular sequence,<br />regular sequence and system of parameters over R-modules. Also we obtain some new results about cofinitness and cominimaxness of local cohomology modules.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101SOME NEW CONSTRUCTIONS OF LINEAR CODES INCLUDING A WIDE FAMILY OF MDS CODES291300159810.22044/jas.2019.7004.1343ENA.RafieepourDepartment of Mathematical Sciences, University of Kashan, P.O. Box 87317-
53153, Kashan, Iran.M.MazrooeiDepartment of Mathematical Sciences, University of Kashan, P.O. Box 87317-
53153, Kashan, Iran.Journal Article20180427Let $mathbb{Z}_p$ be the finite field of integers modulo $p$, where $p>3$ is a prime integer. This paper presents new constructions of linear codes over $mathbb{Z}_p$. Based on our construction, linear codes of length $p-1$, including a wide family of MDS codes, and codes of length $(p-1)^2$ are constructed. we shall discuss the parameters of the codes defined while describing a generator matrix for the first family.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101SERRE SUBCATEGORY, LOCAL HOMOLOGY AND LOCAL COHOMOLOGY301314159710.22044/jas.2019.7430.1366ENS. O.FaramarziDepartment of Mathematics, Payam Noor University (PNU), Tehran, Iran.Z.BarghsouzDepartment of Mathematics, Payam Noor University (PNU), Tehran, Iran.Journal Article20180902We show some results about local homology modules and local cohomology modules concerning to being in a serre sub<br /> category of the category of R-modules. Also for an ideal I of R we define the concept of CI condition on a serre category, which seems dual to CI condition of Melkerson [1]. As a main result we show that for any minimax R-module M of any serre category S that satisifies CI (CI) condition the local homology module HiI(M)<br /> (local cohomology module HIi(M) 2 S) for all i ≥ 0.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101ORDER DENSE ESSENTIALITY AND BEHAVIOR OF ORDER DENSE INJECTIVITY315334159910.22044/jas.2019.7773.1384ENL.ShahbazDepartment of Mathematics, University of Maragheh, P.O. Box 55181-83111, Maragheh,
Iran.Journal Article20181202In this paper, we study the categorical and algebraic properties, such as limits and colimits of the category Pos-S with respect to order dense embeddings. Injectivity with respect to this class of monomorphisms has been studied by the author and used to obtain information about injectivity relative to regular monomorphisms. Then, we study three different kinds of essentiality, usually used in literature, with respect to the class of all order dense embed-dings of S-posets, and investigate their relations to order dense injectivity. We will see, among other things, that although all of these essential extensions<br /> are not necessarily equivalent, they behave equivalently with respect to order dense injectivity. More precisely, it is proved that order dense injectivity well behaves regarding these essentialities. Finally, a characterization of these<br /> essentialities over pogroups is given.