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Algebra and Related Topics - Volume:4 Issue: 2, Autumn 2016

Journal of Algebra and Related Topics
Volume:4 Issue: 2, Autumn 2016

  • تاریخ انتشار: 1395/11/12
  • تعداد عناوین: 6
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  • Z. Sepasdar* Pages 1-8
    A natural generalization of two dimensional cyclic code (\TTDC) is two dimensional skew cyclic codeý. ýIt is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring Rn:=\F[x,y;ρ,θ]/lý. ýIn this paper we characterize the left ideals of the ring Rn with two methods and find the generator matrix for two dimensional skew cyclic codesý.
    Keywords: Cyclic code, two dimensional skew cyclic code, ýgenerator matrix
  • M. Samiei *, H. Fazaeli Moghimi Pages 9-17
    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 Rare also studied.
    Keywords: Weakly irreducible ideal?, ?quasi, primary ?ideal, strongly irreducible ideal
  • T. Amouzegar * Pages 19-29
    Let R be a ring and M a right R-module with S=EndR(M). A module M is called semi-projective if for any epimorphism f:M→N, where N is a submodule of M, and for any homomorphism g:M→N, there exists h:M→M such that fh=g. In this paper, we study SGQ-projective and π-semi-projective modules as two generalizations of semi-projective modules. A module M is called an SGQ-projective module if for any ϕ∈S, there exists a right ideal Xϕ of S such that DS(Iϕ)=ϕS⊕Xϕ as right S-modules. We call M a π-semi-projective module if for any 0≠s∈S, there exists a positive integer n such that sn≠0 and any R-homomorphism from M to snM can be extended to an endomorphism of M. Some properties of this class of modules are investigated.
    Keywords: Semi-projective module, SGQ-projective module, pi-Semi-projective, Coretractable module, Endomorphism ring
  • A. Sahleh*, L. Najarpisheh Pages 31-39
    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 with respect to these properties.
    Keywords: Semitopological semigroup, (universal) semigroup compactification, distal function, weakly almost periodic function, ideal retraction property
  • I. Akray* Pages 41-47
    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∈R with ab∈P−IP implies either a∈P or b∈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.
    Keywords: Prime ideal, weakly prime ideal, almost prime ideal, radical of the ideal
  • H. Mostafanasab* Pages 49-63
    For a finite field Fq, the bivariate skew polynomial ring Fq[x,y;ρ,θ] has been used to study codes \cite{XH}. In this paper, we give some characterizations of the ring R[x,y;ρ,θ], where R is a commutative ring. We investigate 2-D skew (λ1,λ2)-constacyclic codes in the ring R[x,y;ρ,θ]/⟨xl−λ1,ys−λ2⟩l. Also, the dual of 2-D skew (λ1,λ2)-constacyclic codes is investigated.
    Keywords: Cyclic codes, Skew polynomial ringsý, ý2, D skew constacyclic codes