University of GuilanJournal of Algebra and Related Topics2345-39314220161201Some notes on the characterization of two dimensional skew cyclic codes182002ENZ. SepasdarFerdowsi university of MashhadJournal Article20161022A 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.https://jart.guilan.ac.ir/article_2002_7fb571bf92863d300628e203515796fa.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39314220161201Weakly irreducible ideals9172001ENM. SamieiDepartment of Mathematics, Velayat University, Iranshahr, Iran.H. Fazaeli MoghimiDepartment of Mathematics, University of Birjand, Birjand, Iran.Journal Article20160713Let $R$ 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.https://jart.guilan.ac.ir/article_2001_9216f3d6632631978bd0157cd816db85.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39314220161201On two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective19291999ENT. AmouzegarQuchan university of Advanced TechnologyJournal Article20160513Let $R$ 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.https://jart.guilan.ac.ir/article_1999_2bbc92f04935d418d9d7455095e55e83.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39314220161201The universal $mathcal{AIR}$- compactification of a semigroup31392000ENA. SahlehUniversity of GuilanL. NajarpishehUniversity of GuilanJournal Article20160518In 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 with<br />respect to these properties.https://jart.guilan.ac.ir/article_2000_7d9dcf6b892e84c4d861076a1b649e06.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39314220161201I-prime ideals41471998ENI. AkraySoran UniversityJournal Article20160511In 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.https://jart.guilan.ac.ir/article_1998_805b509c5392f49a246ca25b4fb110a2.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-393142201612012-D skew constacyclic codes over R[x, y; ρ, θ]49631997ENH. MostafanasabEski Silahtaraga Elektrik Santrali, Kazim Karabekir, Istanbul Bilgi UniversityJournal Article20160526For 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.https://jart.guilan.ac.ir/article_1997_815df3ed319d9ed34d989ba776bacb95.pdf