Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
SOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP
105
130
EN
S.
Visweswaran
Department of Mathematics, Saurashtra University P.O.Box 360 005, Rajkot, India.
s_visweswaran2006@yahoo.co.in
P.
Vadhel
Department of Mathematics, Saurashtra University P.O.Box 360 005, Rajkot, India.
pravin_2727@yahoo.com
10.22044/jas.2018.5917.1296
Let 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.
Complement of the intersection graph of subgroups of a finite group,finite abelian group,connected graph,girth of a graph
https://jas.shahroodut.ac.ir/article_1583.html
https://jas.shahroodut.ac.ir/article_1583_a9bb297705f77d5027f78b0e6762e92e.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
THE SPECTRAL DETERMINATION OF THE MULTICONE GRAPHS Kw ▽ C WITH RESPECT TO THEIR SIGNLESS LAPLACIAN SPECTRA
131
141
EN
A.
Zeydi Abdian
Department of Mathematical Sciences, Lorestan University, Lorestan, Khoramabad,
Iran.
aabdian67@gmail.com
Gh. H.
Fath-Tabar
Department of Pure Mathematics, Faculty of Mathematical Sciences, University
of Kashan, Kashan 87317-53153, Iran.
fathtabar@kashanu.ac.ir
M.
Rahmani Moghaddam
Department of Mathematics, Bu-Ali Sina University, Hamadan, Iran.
maryam.rahmanimoghadam@gmail.com
10.22044/jas.2018.5879.1292
The 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.
Clebsch graph,DS graph,Signless Laplacian spectra,Multicone graph
https://jas.shahroodut.ac.ir/article_1584.html
https://jas.shahroodut.ac.ir/article_1584_263d68e7f82f30f4fffed73b805e5a47.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING
143
154
EN
H.
Dorbidi
Department of Mathematics, Faculty of Science, University of Jiroft, P.O. Box
78671-61167, Jiroft, Iran.
hr_dorbidi@ujiroft.ac.ir
S.
Alikhani
0000-0002-1801-203X
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
alikhani@yazd.ac.ir
10.22044/jas.2019.7405.1365
In 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 $IJ=I\cap J$. We<br /> obtain some properties of this graph and study its<br /> relation to the structure of $R$.
Graph,diameter,Ring,Idempotent
https://jas.shahroodut.ac.ir/article_1585.html
https://jas.shahroodut.ac.ir/article_1585_0115d6f468b7fb69d3639428ff331638.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
P-CLOSURE IN PSEUDO BCI-ALGEBRAS
155
165
EN
H.
Harizavi
0000-0002-4839-5035
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
harizavi@scu.ac.ir
10.22044/jas.2019.6332.1315
In 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.
Pseudo BCI-algebra,Pseudo BCI-ideal,P-closure,Closure operator
https://jas.shahroodut.ac.ir/article_1586.html
https://jas.shahroodut.ac.ir/article_1586_994b806d9cbd425ae6e15391715c3f04.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
A KIND OF F-INVERSE SPLIT MODULES
167
178
EN
M.
Hosseinpour
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,
P.O. Box 47416-95447, Babolsar, Iran.
mehrab.hosseinpour@gmail.com
A. R.
Moniri Hamzekolaee
0000-0002-2852-7870
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,
P.O. Box 47416-95447, Babolsar, Iran.
a.monirih@umz.ac.ir
10.22044/jas.2019.7211.1353
Let 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.
Rickart module,Z(M)-inverse split module,Z^2(M)-inverse split module
https://jas.shahroodut.ac.ir/article_1587.html
https://jas.shahroodut.ac.ir/article_1587_488e6eda3752698fdd43a0b3c52a0dde.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
179
187
EN
M.
Mohagheghy Nezhad
Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box
1159, Mashhad, Iran.
mostafa.mohaqeqi@mail.um.ac.ir
F.
Rahbarnia
Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box
1159, Mashhad, Iran.
rahbarnia@um.ac.ir
M.
Mirzavaziri
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad, Iran.
mirzavaziri@um.ac.ir
R.
Ghanbari
Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box
1159, Mashhad, Iran.
rghanbari@um.ac.ir
10.22044/jas.2019.7367.1363
The \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.
Metric dimension,Resolving set,Metric basis,Basic distance,Contour of a graph
https://jas.shahroodut.ac.ir/article_1588.html
https://jas.shahroodut.ac.ir/article_1588_14ce71a7aec0d0417b21b3acf6be72d4.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
COMPUTING THE EIGENVALUES OF CAYLEY GRAPHS OF ORDER p2q
189
203
EN
M.
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785-136, I. R. Iran.
mghorbani@sru.ac.ir
A.
Seyyed-Hadi
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785-136, I. R. Iran.
aziz.saidhadi@gmail.com
F.
Nowroozi-Larki
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785-136, I. R. Iran.
fnowroozi@gmail.com
10.22044/jas.2019.7034.1344
A 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.
symmetric graph,Cayley graph,normal graph,arc-transitive graph
https://jas.shahroodut.ac.ir/article_1589.html
https://jas.shahroodut.ac.ir/article_1589_29d397f1277733df32fcf3acd511405d.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
A GENERALIZATION OF PRIME HYPERIDEALS IN KRASNER HYPERRINGS
205
216
EN
L.
Kamali Ardekani
0000-0002-9942-6356
Faculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran.
l.kamali@ardakan.ac.ir
B.
Davvaz
https://orcid.org/00
Department of Mathematics, Yazd University, Yazd, Iran.
davvaz@yazd.ac.ir
10.22044/jas.2019.6407.1318
In 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.
Prime hyperideal,2-absorbing hyperideal,Krasner hyperring
https://jas.shahroodut.ac.ir/article_1590.html
https://jas.shahroodut.ac.ir/article_1590_3ec344babdad88075d27f447c30faa6a.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
EQUALIZERS IN THE CATEGORIES FUZZ AND TOPFUZZ
217
226
EN
Gh.
Mirhosseinkhani
Department of Mathematics and Computer Sciences, Sirjan University of Technology,
Sirjan, Iran.
gh.mirhosseini@yahoo.com
N.
Nazari
Department of Mathematics, University of Hormozgan, Bandarabbas, Iran.
nazarinargesmath@yahoo.com
10.22044/jas.2019.7254.1355
It 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.
Fuzz,Topological fuzz,Molecular lattice,Equalizer
https://jas.shahroodut.ac.ir/article_1591.html
https://jas.shahroodut.ac.ir/article_1591_456819627dfad4d16a4612d7f8c0f596.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
ON SEMICOVERING, SUBSEMICOVERING, AND SUBCOVERING MAPS
227
244
EN
M.
Kowkabi
Department of Mathematics, University of Gonabad, P.O. Box 57678-96919, Gonabad,
Iran.
m.kowkabi@stu.um.ac.ir
B.
Mashayekhi
0000-0001-5243-0641
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-
91775, Mashhad, Iran.
bmashf@um.ac.ir
H.
Torabi
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-
91775, Mashhad, Iran.
h.torabi@ferdowsi.um.ac.ir
10.22044/jas.2019.6941.1367
In 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.
local homeomorphism,fundamental group,covering map,semicovering map subcovering map,subsemicovering map
https://jas.shahroodut.ac.ir/article_1592.html
https://jas.shahroodut.ac.ir/article_1592_46e995b39d0d2f43bc1e0729906f2507.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
ON LOCAL ANTIMAGIC CHROMATIC NUMBER OF GRAPHS
245
256
EN
S.
Shaebani
School of Mathematics and Computer Science, Damghan University, P.O. Box
36716-41167, Damghan, Iran.
shaebani@du.ac.ir
10.22044/jas.2019.7933.1391
A {\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 $\omega _{f}(u)=\sum _{x\in N(u)} f(xu)$. 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].
Antimagic labeling,Local antimagic labeling,Local antimagic chromatic number
https://jas.shahroodut.ac.ir/article_1593.html
https://jas.shahroodut.ac.ir/article_1593_af1188905d11cbb4a0f2430b514d9ffb.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS
257
269
EN
M.
Abedi
0000-0002-8763-4510
Esfarayen University of Technology, Esfarayen, North Khorasan, Iran.
abedi@esfarayen.ac.ir
10.22044/jas.2019.8150.1399
We 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 $Q \cap\mathcal{R}^*L$ 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 $L={\bf2}$.
Frame,primary ideal,pseudo-prime ideal,ring of continuous real-valued functions,decomposable ideal
https://jas.shahroodut.ac.ir/article_1594.html
https://jas.shahroodut.ac.ir/article_1594_8108dcd6f42553890dfb9b0ba2055003.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
A REDUCTION IN THE SEARCH SPACE OF QC-LDPC CODES WITH GIRTH 8
271
280
EN
F.
Amirzade
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood,
Iran.
famirzade@gmail.com
M.
Alishahi
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood,
Iran.
meysam_alishahi@shahroodut.ac.ir
M.R.
Rafsanjani-Sadeghi
Department of Mathematics and Computer Science, Amirkabir University of Technology,
Tehran, Iran.
msadeghi@aut.ac.ir
10.22044/jas.2019.8086.1397
In 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.
QC-LDPC codes,girth,Difference matrices,Lifting degree
https://jas.shahroodut.ac.ir/article_1595.html
https://jas.shahroodut.ac.ir/article_1595_a7ac6815ccabe0982d7a0162bf5de1b0.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
FILTER REGULAR SEQUENCES AND LOCAL COHOMOLOGY MODULES
281
290
EN
J.
Azami
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
jafar.azami@gmail.com
10.22044/jas.2019.7493.1370
Let 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.
Filter regular sequence,Regular sequence,System of parameters
https://jas.shahroodut.ac.ir/article_1596.html
https://jas.shahroodut.ac.ir/article_1596_84472fe9d4e3a9dc676cb38922816c2e.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
SOME NEW CONSTRUCTIONS OF LINEAR CODES INCLUDING A WIDE FAMILY OF MDS CODES
291
300
EN
A.
Rafieepour
Department of Mathematical Sciences, University of Kashan, P.O. Box 87317-
53153, Kashan, Iran.
a.rafieepour@gmail.com
M.
Mazrooei
Department of Mathematical Sciences, University of Kashan, P.O. Box 87317-
53153, Kashan, Iran.
m.mazrooei@kashanu.ac.ir
10.22044/jas.2019.7004.1343
Let $\mathbb{Z}_p$ 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.
Finite Fields,Linear Codes,MDS codes
https://jas.shahroodut.ac.ir/article_1598.html
https://jas.shahroodut.ac.ir/article_1598_8c556522c1aaf88d9e80bdbe10f287f4.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
SERRE SUBCATEGORY, LOCAL HOMOLOGY AND LOCAL COHOMOLOGY
301
314
EN
S. O.
Faramarzi
Department of Mathematics, Payam Noor University (PNU), Tehran, Iran.
s.o.faramarzi@gmail.com
Z.
Barghsouz
Department of Mathematics, Payam Noor University (PNU), Tehran, Iran.
zbarghsooz@gmail.com
10.22044/jas.2019.7430.1366
We 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.
local homology,Local cohomology,Serre category
https://jas.shahroodut.ac.ir/article_1597.html
https://jas.shahroodut.ac.ir/article_1597_067f1dfdd98a689c0c7d5492964b4236.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
7
2
2020
01
01
ORDER DENSE ESSENTIALITY AND BEHAVIOR OF ORDER DENSE INJECTIVITY
315
334
EN
L.
Shahbaz
0000-0001-6312-6231
Department of Mathematics, University of Maragheh, P.O. Box 55181-83111, Maragheh,
Iran.
leilashahbaz@yahoo.com
10.22044/jas.2019.7773.1384
In 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.
S-poset,order dense sub S-poset,od-injective,od-essential
https://jas.shahroodut.ac.ir/article_1599.html
https://jas.shahroodut.ac.ir/article_1599_d0959f964f88150ce83fb33f24492605.pdf