eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
105
130
10.22044/jas.2018.5917.1296
1583
SOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP
S. Visweswaran
s_visweswaran2006@yahoo.co.in
1
P. Vadhel
pravin_2727@yahoo.com
2
Department of Mathematics, Saurashtra University P.O.Box 360 005, Rajkot, India.
Department of Mathematics, Saurashtra University P.O.Box 360 005, Rajkot, India.
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.
http://jas.shahroodut.ac.ir/article_1583_a9bb297705f77d5027f78b0e6762e92e.pdf
Complement of the intersection graph of subgroups of a finite group
finite abelian group
connected graph
girth of a graph
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
131
141
10.22044/jas.2018.5879.1292
1584
THE SPECTRAL DETERMINATION OF THE MULTICONE GRAPHS Kw ▽ C WITH RESPECT TO THEIR SIGNLESS LAPLACIAN SPECTRA
A. Zeydi Abdian
aabdian67@gmail.com
1
Gh. H. Fath-Tabar
fathtabar@kashanu.ac.ir
2
M. Rahmani Moghaddam
maryam.rahmanimoghadam@gmail.com
3
Department of Mathematical Sciences, Lorestan University, Lorestan, Khoramabad, Iran.
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran.
Department of Mathematics, Bu-Ali Sina University, Hamadan, Iran.
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.
http://jas.shahroodut.ac.ir/article_1584_263d68e7f82f30f4fffed73b805e5a47.pdf
Clebsch graph
DS graph
Signless Laplacian spectra
Multicone graph
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
143
154
10.22044/jas.2019.7405.1365
1585
A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING
H. Dorbidi
hr_dorbidi@ujiroft.ac.ir
1
S. Alikhani
alikhani@yazd.ac.ir
2
Department of Mathematics, Faculty of Science, University of Jiroft, P.O. Box 78671-61167, Jiroft, Iran.
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
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 $IJ=Icap J$. We<br /> obtain some properties of this graph and study its<br /> relation to the structure of $R$.
http://jas.shahroodut.ac.ir/article_1585_0115d6f468b7fb69d3639428ff331638.pdf
Graph
diameter
Ring
Idempotent
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
155
165
10.22044/jas.2019.6332.1315
1586
P-CLOSURE IN PSEUDO BCI-ALGEBRAS
H. Harizavi
harizavi@scu.ac.ir
1
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
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.
http://jas.shahroodut.ac.ir/article_1586_994b806d9cbd425ae6e15391715c3f04.pdf
Pseudo BCI-algebra
Pseudo BCI-ideal
P-closure
Closure operator
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
167
178
10.22044/jas.2019.7211.1353
1587
A KIND OF F-INVERSE SPLIT MODULES
M. Hosseinpour
mehrab.hosseinpour@gmail.com
1
A. R. Moniri Hamzekolaee
a.monirih@umz.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran.
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.
http://jas.shahroodut.ac.ir/article_1587_488e6eda3752698fdd43a0b3c52a0dde.pdf
Rickart module
Z(M)-inverse split module
Z^2(M)-inverse split module
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
179
187
10.22044/jas.2019.7367.1363
1588
A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
M. Mohagheghy Nezhad
mostafa.mohaqeqi@mail.um.ac.ir
1
F. Rahbarnia
rahbarnia@um.ac.ir
2
M. Mirzavaziri
mirzavaziri@um.ac.ir
3
R. Ghanbari
rghanbari@um.ac.ir
4
Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
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.
http://jas.shahroodut.ac.ir/article_1588_14ce71a7aec0d0417b21b3acf6be72d4.pdf
Metric dimension
Resolving set
Metric basis
Basic distance
Contour of a graph
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
189
203
10.22044/jas.2019.7034.1344
1589
COMPUTING THE EIGENVALUES OF CAYLEY GRAPHS OF ORDER p2q
M. Ghorbani
mghorbani@sru.ac.ir
1
A. Seyyed-Hadi
aziz.saidhadi@gmail.com
2
F. Nowroozi-Larki
fnowroozi@gmail.com
3
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, I. R. Iran.
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, I. R. Iran.
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, I. R. Iran.
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.
http://jas.shahroodut.ac.ir/article_1589_29d397f1277733df32fcf3acd511405d.pdf
symmetric graph
Cayley graph
normal graph
arc-transitive graph
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
205
216
10.22044/jas.2019.6407.1318
1590
A GENERALIZATION OF PRIME HYPERIDEALS IN KRASNER HYPERRINGS
L. Kamali Ardekani
l.kamali@ardakan.ac.ir
1
B. Davvaz
davvaz@yazd.ac.ir
2
Faculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran.
Department of Mathematics, Yazd University, Yazd, Iran.
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.
http://jas.shahroodut.ac.ir/article_1590_3ec344babdad88075d27f447c30faa6a.pdf
Prime hyperideal
2-absorbing hyperideal
Krasner hyperring
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
217
226
10.22044/jas.2019.7254.1355
1591
EQUALIZERS IN THE CATEGORIES FUZZ AND TOPFUZZ
Gh. Mirhosseinkhani
gh.mirhosseini@yahoo.com
1
N. Nazari
nazarinargesmath@yahoo.com
2
Department of Mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran.
Department of Mathematics, University of Hormozgan, Bandarabbas, Iran.
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.
http://jas.shahroodut.ac.ir/article_1591_456819627dfad4d16a4612d7f8c0f596.pdf
Fuzz
Topological fuzz
Molecular lattice
Equalizer
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
227
244
10.22044/jas.2019.6941.1367
1592
ON SEMICOVERING, SUBSEMICOVERING, AND SUBCOVERING MAPS
M. Kowkabi
m.kowkabi@stu.um.ac.ir
1
B. Mashayekhi
bmashf@um.ac.ir
2
H. Torabi
h.torabi@ferdowsi.um.ac.ir
3
Department of Mathematics, University of Gonabad, P.O. Box 57678-96919, Gonabad, Iran.
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159- 91775, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159- 91775, Mashhad, Iran.
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.
http://jas.shahroodut.ac.ir/article_1592_46e995b39d0d2f43bc1e0729906f2507.pdf
local homeomorphism
fundamental group
covering map
semicovering map subcovering map
subsemicovering map
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
245
256
10.22044/jas.2019.7933.1391
1593
ON LOCAL ANTIMAGIC CHROMATIC NUMBER OF GRAPHS
S. Shaebani
shaebani@du.ac.ir
1
School of Mathematics and Computer Science, Damghan University, P.O. Box 36716-41167, Damghan, Iran.
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 $omega _{f}(u)=sum _{xin N(u)} f(xu)$. 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].
http://jas.shahroodut.ac.ir/article_1593_af1188905d11cbb4a0f2430b514d9ffb.pdf
Antimagic labeling
Local antimagic labeling
Local antimagic chromatic number
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
257
269
10.22044/jas.2019.8150.1399
1594
ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS
M. Abedi
abedi@esfarayen.ac.ir
1
Esfarayen University of Technology, Esfarayen, North Khorasan, Iran.
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 $Q capmathcal{R}^*L$ 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 $L={bf2}$.
http://jas.shahroodut.ac.ir/article_1594_8108dcd6f42553890dfb9b0ba2055003.pdf
Frame
primary ideal
pseudo-prime ideal
ring of continuous real-valued functions
decomposable ideal
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
271
280
10.22044/jas.2019.8086.1397
1595
A REDUCTION IN THE SEARCH SPACE OF QC-LDPC CODES WITH GIRTH 8
F. Amirzade
famirzade@gmail.com
1
M. Alishahi
meysam_alishahi@shahroodut.ac.ir
2
M.R. Rafsanjani-Sadeghi
msadeghi@aut.ac.ir
3
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.
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.
http://jas.shahroodut.ac.ir/article_1595_a7ac6815ccabe0982d7a0162bf5de1b0.pdf
QC-LDPC codes
girth
Difference matrices
Lifting degree
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
281
290
10.22044/jas.2019.7493.1370
1596
FILTER REGULAR SEQUENCES AND LOCAL COHOMOLOGY MODULES
J. Azami
jafar.azami@gmail.com
1
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
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.
http://jas.shahroodut.ac.ir/article_1596_84472fe9d4e3a9dc676cb38922816c2e.pdf
Filter regular sequence
Regular sequence
System of parameters
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
291
300
10.22044/jas.2019.7004.1343
1598
SOME NEW CONSTRUCTIONS OF LINEAR CODES INCLUDING A WIDE FAMILY OF MDS CODES
A. Rafieepour
a.rafieepour@gmail.com
1
M. Mazrooei
m.mazrooei@kashanu.ac.ir
2
Department of Mathematical Sciences, University of Kashan, P.O. Box 87317- 53153, Kashan, Iran.
Department of Mathematical Sciences, University of Kashan, P.O. Box 87317- 53153, Kashan, Iran.
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.
http://jas.shahroodut.ac.ir/article_1598_8c556522c1aaf88d9e80bdbe10f287f4.pdf
Finite Fields
Linear Codes
MDS codes
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
301
314
10.22044/jas.2019.7430.1366
1597
SERRE SUBCATEGORY, LOCAL HOMOLOGY AND LOCAL COHOMOLOGY
S. O. Faramarzi
s.o.faramarzi@gmail.com
1
Z. Barghsouz
zbarghsooz@gmail.com
2
Department of Mathematics, Payam Noor University (PNU), Tehran, Iran.
Department of Mathematics, Payam Noor University (PNU), Tehran, Iran.
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.
http://jas.shahroodut.ac.ir/article_1597_067f1dfdd98a689c0c7d5492964b4236.pdf
local homology
Local cohomology
Serre category
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2020-01-01
7
2
315
334
10.22044/jas.2019.7773.1384
1599
ORDER DENSE ESSENTIALITY AND BEHAVIOR OF ORDER DENSE INJECTIVITY
L. Shahbaz
leilashahbaz@yahoo.com
1
Department of Mathematics, University of Maragheh, P.O. Box 55181-83111, Maragheh, Iran.
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.
http://jas.shahroodut.ac.ir/article_1599_d0959f964f88150ce83fb33f24492605.pdf
S-poset
order dense sub S-poset
od-injective
od-essential