2017-12-11T03:35:27Z
http://jart.guilan.ac.ir/?_action=export&rf=summon&issue=390
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
2
Some notes on the characterization of two dimensional skew cyclic codes
Z.
Sepasdar
A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code. It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$. In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional skew cyclic codes.
Cyclic code
two dimensional skew cyclic code
generator matrix
2016
12
01
1
8
http://jart.guilan.ac.ir/article_2002_7fb571bf92863d300628e203515796fa.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
2
Weakly irreducible ideals
M.
Samiei
H.
Fazaeli Moghimi
Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has been given. Also the relations between weakly irreducible ideals of $R$ and weakly irreducible ideals of localizations of the ring $R$ are also studied.
Weakly irreducible ideal
quasi-primary ideal
strongly irreducible ideal
2016
12
01
9
17
http://jart.guilan.ac.ir/article_2001_9216f3d6632631978bd0157cd816db85.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
2
On two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective
T.
Amouzegar
Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A module $M$ is called an SGQ-projective module if for any $phiin S$, there exists a right ideal $X_phi$ of $S$ such that $D_S(Im phi)=phi Soplus X_phi$ as right $S$-modules. We call $M$ a $pi$-semi-projective module if for any $0neq sin S$, there exists a positive integer $n$ such that $s^nneq 0$ and any $R$-homomorphism from $M$ to $s^nM$ can be extended to an endomorphism of $M$. Some properties of this class of modules are investigated.
Semi-projective module
SGQ-projective module
$pi$-Semi-projective
Coretractable module
Endomorphism ring
2016
12
01
19
29
http://jart.guilan.ac.ir/article_1999_2bbc92f04935d418d9d7455095e55e83.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
2
The universal $mathcal{AIR}$- compactification of a semigroup
A.
Sahleh
L.
Najarpisheh
In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.
Semitopological semigroup
(universal) semigroup compactification
distal function
weakly almost periodic function
ideal retraction property
2016
12
01
31
39
http://jart.guilan.ac.ir/article_2000_7d9dcf6b892e84c4d861076a1b649e06.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
2
I-prime ideals
I.
Akray
In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties. Moreover, we give conditions under which $I$-prime ideals becomes prime or weakly prime and we construct the view of $I$-prime ideal in decomposite rings.
Prime ideal
weakly prime ideal
almost prime ideal
radical of the ideal
2016
12
01
41
47
http://jart.guilan.ac.ir/article_1998_805b509c5392f49a246ca25b4fb110a2.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
2
2-D skew constacyclic codes over R[x, y; ρ, θ]
H.
Mostafanasab
For a finite field $mathbb{F}_q$, the bivariate skew polynomial ring $mathbb{F}_q[x,y;rho,theta]$ has been used to study codes cite{XH}. In this paper, we give some characterizations of the ring $R[x,y;rho,theta]$, where $R$ is a commutative ring. We investigate 2-D skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $R[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ Also, the dual of 2-D skew $(lambda_1,lambda_2)$-constacyclic codes is investigated.
Cyclic codes
Skew polynomial rings
2-D skew constacyclic codes
2016
12
01
49
63
http://jart.guilan.ac.ir/article_1997_815df3ed319d9ed34d989ba776bacb95.pdf