Some notes on the characterization of two dimensional skew cyclic codes
Z.
Sepasdar
Ferdowsi university of Mashhad
author
text
article
2016
eng
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 $R_n:=\F[x,y;\rho,\theta]/<x^s-1, y^\ell-1>_l$. 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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
2
no.
2016
1
8
https://jart.guilan.ac.ir/article_2002_7fb571bf92863d300628e203515796fa.pdf
Weakly irreducible ideals
M.
Samiei
Department of Mathematics, Velayat University, Iranshahr, Iran.
author
H.
Fazaeli Moghimi
Department of Mathematics, University of Birjand, Birjand, Iran.
author
text
article
2016
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
2
no.
2016
9
17
https://jart.guilan.ac.ir/article_2001_9216f3d6632631978bd0157cd816db85.pdf
On two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective
T.
Amouzegar
Quchan university of Advanced Technology
author
text
article
2016
eng
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 $f:M\rightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: M\rightarrow N$, there exists $h:M\rightarrow M$ 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 $\phi\in S$, there exists a right ideal $X_\phi$ of $S$ such that $D_S(\Im \phi)=\phi S\oplus X_\phi$ as right $S$-modules. We call $M$ a $\pi$-semi-projective module if for any $0\neq s\in S$, there exists a positive integer $n$ such that $s^n\neq 0$ 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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
2
no.
2016
19
29
https://jart.guilan.ac.ir/article_1999_2bbc92f04935d418d9d7455095e55e83.pdf
The universal $\mathcal{AIR}$- compactification of a semigroup
A.
Sahleh
University of Guilan
author
L.
Najarpisheh
University of Guilan
author
text
article
2016
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
2
no.
2016
31
39
https://jart.guilan.ac.ir/article_2000_7d9dcf6b892e84c4d861076a1b649e06.pdf
I-prime ideals
I.
Akray
Soran University
author
text
article
2016
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
2
no.
2016
41
47
https://jart.guilan.ac.ir/article_1998_805b509c5392f49a246ca25b4fb110a2.pdf
2-D skew constacyclic codes over R[x, y; ρ, θ]
H.
Mostafanasab
Eski Silahtaraga Elektrik Santrali, Kazim Karabekir, Istanbul Bilgi University
author
text
article
2016
eng
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 $R[x,y;\rho,\theta]/\langle x^l-\lambda_1,y^s-\lambda_2\rangle_{\mathit{l}}.$ Also, the dual of 2-D skew $(\lambda_1,\lambda_2)$-constacyclic codes is investigated.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
2
no.
2016
49
63
https://jart.guilan.ac.ir/article_1997_815df3ed319d9ed34d989ba776bacb95.pdf