##### ϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES

M. Rahmatinia; A. Yousefian Darani

Volume 8, Issue 2 , January 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

##### TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES

A. R. Nazari; F. Rastgoo

Volume 8, Issue 2 , January 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

##### SOME CLASSIFICATIONS OF MONOIDS BY VARIOUS NOTIONS OF INJECTIVITY OF ACTS

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

Volume 8, Issue 2 , January 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

##### CONTINUOUS FUNCTIONS ON LG-SPACES

Volume 8, Issue 2 , January 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

##### A NOTE ON BALANCED BIG COHEN–MACAULAY MODULES

Abdol N. Bahlekeh

Volume 8, Issue 2 , January 2021, Pages 201-207

##### HOOPS WITH QUASI-VALUATION MAPS

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

Volume 8, Issue 2 , January 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

##### LINKAGE OF IDEALS OVER A MODULE

M. Jahangiri; Kh. Sayyari

Volume 8, Issue 2 , January 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

##### 4-CYCLE FREE APM LDPC CODES WITH AN EXPLICIT CONSTRUCTION

Z. Gholami; M. Gholami

Volume 8, Issue 2 , January 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

##### ON THE CLASS OF ARRAY-BASED APM-LDPC CODES

A. Nassaj; A. R. Naghipour

Volume 8, Issue 2 , January 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