@Article{Sepasdar2016,
author="Sepasdar, Z.",
title="Some notes on the characterization of two dimensional skew cyclic codes",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="2",
pages="1-8",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_2002.html"
}
@Article{Samiei2016,
author="Samiei, M.
and Fazaeli Moghimi, H.",
title="Weakly irreducible ideals",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="2",
pages="9-17",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_2001.html"
}
@Article{Amouzegar2016,
author="Amouzegar, T.",
title="On two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="2",
pages="19-29",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1999.html"
}
@Article{Sahleh2016,
author="Sahleh, A.
and Najarpisheh, L.",
title="The universal $\mathcal{AIR}$- compactification of a semigroup",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="2",
pages="31-39",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_2000.html"
}
@Article{Akray2016,
author="Akray, I.",
title="I-prime ideals",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="2",
pages="41-47",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1998.html"
}
@Article{Mostafanasab2016,
author="Mostafanasab, H.",
title="2-D skew constacyclic codes over R[x, y; ρ, θ]",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="2",
pages="49-63",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1997.html"
}