1. ϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES

M. Rahmatinia; A. Yousefian Darani

Volume 8, Issue 2 , Winter and Spring 2021, Pages 141-154

Abstract
  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 ...  Read More

2. TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES

A. R. Nazari; F. Rastgoo

Volume 8, Issue 2 , Winter and Spring 2021, Pages 155-164

Abstract
  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 AsshR M, then there exists an ideal a of R such ...  Read More

3. SOME CLASSIFICATIONS OF MONOIDS BY VARIOUS NOTIONS OF INJECTIVITY OF ACTS

M. Roueentan; M. Ershad; M. A. Naghipoor

Volume 8, Issue 2 , Winter and Spring 2021, Pages 165-180

Abstract
  This paper is a continuation of recent researches concerning generalization of injectivity of acts over moniods, namely, C-injectivity and InD-injectivity. We introduce new kinds of injectivity, such as, LC-injectivity and CQ-injectivity. Classi cations of monoids by properties of these kinds of injective ...  Read More

4. CONTINUOUS FUNCTIONS ON LG-SPACES

A. Rezai Aliabad; H. Zarepour

Volume 8, Issue 2 , Winter and Spring 2021, Pages 181-200

Abstract
  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, { Bull. Iran. Math. Soc}., 41 (1), (2015), 239-258]. ...  Read More

5. A NOTE ON BALANCED BIG COHEN–MACAULAY MODULES

Abdol N. Bahlekeh

Volume 8, Issue 2 , Winter and Spring 2021, Pages 201-207

Abstract
  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 $ ...  Read More

6. THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH

S. Alikhani; S. Soltani

Volume 8, Issue 2 , Winter and Spring 2021, Pages 209-217

Abstract
  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 ...  Read More

7. ON REGULAR PRIME INJECTIVITY OF S-POSETS

H. Rasouli; Gh. R. Moghaddasi; N. Sarvghad

Volume 8, Issue 2 , Winter and Spring 2021, Pages 219-230

Abstract
  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 ...  Read More

8. NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS

A. Alhevaz; M. Baghipur; S. Paul

Volume 8, Issue 2 , Winter and Spring 2021, Pages 231-250

Abstract
  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 ...  Read More

9. HOOPS WITH QUASI-VALUATION MAPS

M. Aaly Kologani; G. R. Rezaei; R. A. Borzooei; Y. B. Jun

Volume 8, Issue 2 , Winter and Spring 2021, Pages 251-268

Abstract
  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 ...  Read More

10. LINKAGE OF IDEALS OVER A MODULE

M. Jahangiri; Kh. Sayyari

Volume 8, Issue 2 , Winter and Spring 2021, Pages 269-281

Abstract
  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 ...  Read More

11. 4-CYCLE FREE APM LDPC CODES WITH AN EXPLICIT CONSTRUCTION

Z. Gholami; M. Gholami

Volume 8, Issue 2 , Winter and Spring 2021, Pages 283-289

Abstract
  Recently, a class of low-density parity-check codes based on affine permutation matrices, called APM-LDPC codes, 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 ...  Read More

12. ON THE CLASS OF ARRAY-BASED APM-LDPC CODES

A. Nassaj; A. R. Naghipour

Volume 8, Issue 2 , Winter and Spring 2021, Pages 291-301

Abstract
  We construct an explicit class of affine permutation matrix low-density parity-check (APM-LDPC) codes based on the array parity-check matrix by using two affine maps f (x) = x-1 and g(x) = 2x-1 on Z_m, where m is an odd prime number, with girth 6 and flexible row (column)-weights. Simulation results ...  Read More