Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
ϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES
141
154
EN
M.
Rahmatinia
Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179,
Ardabil, Iran.
mahdi.rahmatinia@gmail.com
A.
Yousefian Darani
Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179,
Ardabil, Iran.
youseffian@gmail.com
10.22044/jas.2019.8245.1402
The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and obtain the relationship between $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules.
ϕ-almost Dedekind ring,ϕ-Dedekind ring,Phi-almost Dedekind module,Phi-Dedekind module
https://jas.shahroodut.ac.ir/article_1942.html
https://jas.shahroodut.ac.ir/article_1942_b410589f562e99ad20f1a4a2010554ce.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES
155
164
EN
A. R.
Nazari
Department of Mathematics, Lorestan University, P.O. Box 68151-44316, Khorram
Abad, Iran.
nazari.ar@lu.ac.ir
F.
Rastgoo
Department of Mathematics, Lorestan University, P.O. Box 68151-44316, Khorram
Abad, Iran.
rastgoo.fa@fs.lu.ac.ir
10.22044/jas.2020.8830.1428
Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of Assh<sub>R</sub> M, then there exists an ideal a of R such that Att<sub>R </sub>H<sup>n</sup>a<sup> </sup>(M)=T. As an application, we give some relationships between top local cohomology modules and top formal local cohomology modules.
Attached primes,Local cohomology modules,Formal local cohomology modules,Noetherian local rings
https://jas.shahroodut.ac.ir/article_1943.html
https://jas.shahroodut.ac.ir/article_1943_da72761077b57d04a475692cca69518c.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
SOME CLASSIFICATIONS OF MONOIDS BY VARIOUS NOTIONS OF INJECTIVITY OF ACTS
165
180
EN
M.
Roueentan
Lamerd Higher Education Center, Lamerd, Iran.
m.rooeintan@yahoo.com
M.
Ershad
Department of Mathematics, College of Sciences, Shiraz University, P.O. Box
71454, Shiraz, Iran.
ershad@shirazu.ac.ir
M. A.
Naghipoor
Department of Mathematics, Jahrom University, P.O. Box 74135-11, Jahrom, Iran.
ma_naghipoor@yahoo.com
10.22044/jas.2020.8626.1417
This paper is a continuation of recent researches concerning generalization of<br /> injectivity of acts over moniods, namely, C-injectivity and InD-injectivity. We introduce new<br /> kinds of injectivity, such as, LC-injectivity and CQ-injectivity. Classications of monoids<br /> by properties of these kinds of injective acts are presented. It is proved that a monoid S<br /> is completely (cyclic) injective if and only if it is completely quasi (CQ-) injective. Some<br /> results on quasi-injective acts are proved. Also new characterizations for right hereditary<br /> monoids and right PP-monoids are given.
Locally cyclic (weakly) injective act,Indecomposable (weakly) injective act,C- injective act
https://jas.shahroodut.ac.ir/article_1945.html
https://jas.shahroodut.ac.ir/article_1945_b1855eba786ac9866d194c4f31fa871a.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
CONTINUOUS FUNCTIONS ON LG-SPACES
181
200
EN
A.
Rezai Aliabad
0000-0003-1293-3652
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
aliabady_r@scu.ac.ir
H.
Zarepour
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
ho.zarepour@gmail.com
10.22044/jas.2020.9599.1471
By an $l$-generalized topological space, briefly an $LG$-space, we mean the ordered pair $(F,\tau)$ in which $F$ is a frame and $\tau$ is a subframe of $F$. This notion has been first introduced by A.R. Aliabad and A. Sheykhmiri in [$LG$-topology, { <em>Bull</em>. Iran. Math. Soc}., <strong>41</strong> (1), (2015), 239-258]. In this article, we define continuous functions on $LG$-spaces and determine conditions under which the continuous image of a compact element of an $LG$-space is compact. Moreover, we introduce the concept of connectedness for $LG$-spaces and determine conditions under which the continuous image of a connected element of an $LG$-space is connected. In fact, we show that $LG$-spaces are models for topological spaces as well as frames are models for topologies.
Frame,LG-space,compact element,adjoint mapping,continuous mapping
https://jas.shahroodut.ac.ir/article_1946.html
https://jas.shahroodut.ac.ir/article_1946_7d3a53aeb6d47e5f5a2125390f974935.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
A NOTE ON BALANCED BIG COHEN–MACAULAY MODULES
201
207
EN
Abdol N.
Bahlekeh
Department of Mathematics, Gonbad Kavous University, P.O. Box 4971799151,
Gonbad Kavous, Iran.
n.bahlekeh@gmail.com
10.22044/jas.2020.9007.1438
Let $(R, m, k)$ be a Cohen-Macaulay complete local ring with the canonical module $\omega$. The aim of this note, is to show that, under mild assumptions, the class of balanced big Cohen--Macaulay modules coincides with the one consisting of those modules admitting a right resolution by modules in $ Add\omega$. This generalizes the well-known result for the class of maximal Cohen--Macaulay modules.
maximal Cohen-Macaulay modules,balanced big Cohen-Macaulay modules,canonical module
https://jas.shahroodut.ac.ir/article_1947.html
https://jas.shahroodut.ac.ir/article_1947_e3aec16656301bf5535c8b9412238431.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH
209
217
EN
S.
Alikhani
0000-0002-1801-203X
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
alikhani@yazd.ac.ir
S.
Soltani
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
ssoltani1997@gmail.com
10.22044/jas.2020.8343.1408
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The minimum size of a label class in such a labeling of $G$ with $D(G) = d$ is called the cost of $d$-distinguishing $G$ and is denoted by $\rho_d(G)$. A set of vertices $S\subseteq V(G)$ is a determining set for $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The determining number of $G$, ${\rm Det}(G)$, is the minimum cardinality of determining sets of $G$. In this paper we compute the cost and the determining number for the friendship graphs and corona product of two graphs.
Distinguishing number,distinguishing labeling,determining set
https://jas.shahroodut.ac.ir/article_1948.html
https://jas.shahroodut.ac.ir/article_1948_8ed554351047fe89af7fd04bb8a07ed1.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
ON REGULAR PRIME INJECTIVITY OF S-POSETS
219
230
EN
H.
Rasouli
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
hrasouli@srbiau.ac.ir
Gh. R.
Moghaddasi
Department of Mathematics, Science and Research Branch, Islamic Azad University,
Tehran, Iran.
r.moghadasi@hsu.ac.ir
N.
Sarvghad
Department of Mathematics, Hakim Sabzevary University, Sabzevar, Iran.
n.sarvghad@hsu.ac.ir
10.22044/jas.2020.8317.1406
In this paper, we define the notion of regular prime monomorphism for $S$-posets over a pomonoid $S$ and investigate some categorical properties including products, coproducts and pullbacks. We study $\mathcal{M}$-injectivity in the category of $S$-posets where $\mathcal{M}$ is the class of regular prime monomorphisms and show that the Skornjakov criterion fails for the regular prime injectivity. Considering a weaker form of such kind of injectivity, we obtain some classifications for pomonoids.
prime sub $S$-poset,regular prime monomorphism,regular prime injective
https://jas.shahroodut.ac.ir/article_1949.html
https://jas.shahroodut.ac.ir/article_1949_aad563a0d2447906c778a74bfd257d37.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS
231
250
EN
A.
Alhevaz
0000-0001-6167-607X
Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box:
316-3619995161, Shahrood, Iran.
a.alhevaz@gmail.com
M.
Baghipur
0000-0002-9069-9243
Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar
Abbas, Iran.
maryamb8989@gmail.com
S.
Paul
Department of Applied Sciences, Tezpur University, Tezpur-784028, India.
somnath.paul60@gmail.com
10.22044/jas.2020.9540.1469
The distance signless Laplacian spectral radius of a connected graph $G$ is the largest eigenvalue of the distance signless Laplacian matrix of $G$, defined as $D^{Q}(G)=Tr(G)+D(G)$, where $D(G)$ is the distance matrix of $G$ and $Tr(G)$ is the diagonal matrix of vertex transmissions of $G$. In this paper, we determine some new upper and lower bounds on the distance signless Laplacian spectral radius of $G$ and characterize the extremal graphs attaining these bounds.
Distance signless Laplacian matrix,spectral radius,extremal graph,transmission regular graph
https://jas.shahroodut.ac.ir/article_1954.html
https://jas.shahroodut.ac.ir/article_1954_3d76b11a1deafa958368655d5c44160b.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
HOOPS WITH QUASI-VALUATION MAPS
251
268
EN
M.
Aaly Kologani
Hatef Higher Education Institute, P.O. Box 9816848165, Zahedan, Iran.
mona4011@gmail.com
G. R.
Rezaei
Department of Mathematics, University of Sistan and Baluchestan, P.O. Box 98167-
45845, Zahedan, Iran.
grezaei@math.usb.ac.ir
R. A.
Borzooei
0000-0001-7538-7885
Department of Mathematics, Shahid Beheshti University, P.O. Box 1983969411,
Tehran, Iran.
borzooei@sbu.ac.ir
Y. B.
Jun
0000-0002-0181-8969
Department of Mathematics, Education, Gyeongsang National University, P.O.
Box 52828, Jinju, Korea.
skywine@gmail.com
10.22044/jas.2020.8499.1413
Based on subalgebras and filters in hoops, the notions of S-quasi-valuation maps and F-quasi-valuation maps are introduced, and related properties are investigated. Relations between S-quasi-valuation maps and F-quasi-valuation maps are introduced. Using F-quasi-valuation map, a (pseudo) metric space is indued, and we show that the operations “⊙”, “→” and “∧” in a hoop are uniformly continuous.
Hoop,quasi-valuation map,S⊙(S→,F)-quasi-valuation map,(pseudo) metric space
https://jas.shahroodut.ac.ir/article_1955.html
https://jas.shahroodut.ac.ir/article_1955_ce7dc383760b98c224e268740b53e849.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
LINKAGE OF IDEALS OVER A MODULE
269
281
EN
M.
Jahangiri
Faculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box
1561836314, Tehran, Iran.
mjahangiri@ipm.ir
Kh.
Sayyari
Faculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box
1561836314, Tehran, Iran.
Email: sayyarikh@gmail.
std_sayyari@khu.ac.ir
10.22044/jas.2020.9180.1447
Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered. Specially, we make some extensions and generalizations of a basic result of Peskine and Szpiro \cite[Proposition 1.3]{PS}, namely if $R$ is a Gorenstein local ring, $ a \neq 0$ (an ideal of $R$) and $ b := 0:_R a$ then $\frac{R}{a}$ is Cohen-Macaulay if and only if $\frac{R}{a}$ is unmixed and $\frac{R}{ b}$ is Cohen-Macaulay.
Linkage of ideals,Cohen-Macaulay modules,canonical module
https://jas.shahroodut.ac.ir/article_1956.html
https://jas.shahroodut.ac.ir/article_1956_05388a6d1c144832a0ff693aef3886a5.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
4-CYCLE FREE APM LDPC CODES WITH AN EXPLICIT CONSTRUCTION
283
289
EN
Z.
Gholami
Department of Mathematics, University of Shahrekord, P.O. Box 8818634141, Shahrekord,
Iran.
zghbaba123@gmail.com
M.
Gholami
0000-0002-3174-0138
Department of Mathematics, University of Shahrekord, P.O. Box 8818634141, Shahrekord,
Iran.
gholami-m@sci.sku.ac.ir
10.22044/jas.2020.9086.1441
Recently, a class of low-density parity-check codes<br /> based on affine permutation matrices, called APM-LDPC codes,<br /> have been considered which have some advantages than quasi-cyclic (QC) LDPC codes in terms of minimum-distance, cycle distribution, and error-rate performance. Moreover, some explicit constructions for exponent matrices of conventional APM-LDPC codes<br /> with girth at least 6 have been investigated. In this paper, a class<br /> of 4-cycle free APM-LDPC codes is constructed by a new explicit<br /> method such that the constructed codes have better cycle distributions rather than the recently proposed APM codes with girth 6.<br /> As simulation results show, the constructed codes outperform PEG<br /> and random-like LDPC codes with the same rates and lengths.
APM-LDPC codes,explicit constructions,girth
https://jas.shahroodut.ac.ir/article_1957.html
https://jas.shahroodut.ac.ir/article_1957_2e7bbb3d01640a654c06d6c41e61cedd.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
8
2
2021
01
01
ON THE CLASS OF ARRAY-BASED APM-LDPC CODES
291
301
EN
A.
Nassaj
Mathematics, Sharekord University, Sharekord, Iran
akramnassaj@gmail.com
A. R.
Naghipour
Faculty of Methematical Sciences
Shahrekord University,
Shahrekord, Iran
naghipour@sci.sku.ac.ir
10.22044/jas.2020.8875.1431
We construct an explicit class of affine permutation<br /> matrix low-density parity-check (APM-LDPC) codes based on the<br /> array parity-check matrix by using two affine maps f (x) = x-1 and<br /> g(x) = 2x-1 on Z_m, where m is an odd prime number, with girth 6<br /> and flexible row (column)-weights. Simulation results justify well<br /> performance, minimum-distances and cycle distribution of these<br /> codes in comparison the array-LDPC , structured QC-LDPC and<br /> APM-LDPC.
APM-LDPC code,Array-LDPC code,Tanner graph
https://jas.shahroodut.ac.ir/article_1958.html
https://jas.shahroodut.ac.ir/article_1958_38d83141b35b9fcbbb6bfd5837381e38.pdf