فهرست مطالب
Journal of Algebra and Related Topics
Volume:3 Issue: 1, Summer 2015
- تاریخ انتشار: 1394/02/27
- تعداد عناوین: 6
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Pages 1-11Let R be a commutative ring with identity. Let G(R) denote the maximal graph associated to R, i.e., G(R) is a graph with vertices as the elements of R, where two distinct vertices a and b are adjacent if and only if there is a maximal ideal of R containing both. Let Γ(R) denote the restriction of G(R) to non-unit elements of R. In this paper we study the various graphical properties of the line graph associated to Γ(R), denoted by (Γ(R)) such that diameter, completeness, and Eulerian property. A complete characterization of rings is given for which diam(L(Γ(R)))=diam(Γ(R)) or diam(L(Γ(R)))diam(Γ(R)). We have shown that the complement of the maximal graph G(R), i.e., the comaximal graph is a Euler graph if and only if R
has odd cardinality. We also discuss the Eulerian property of the line graph associated to the comaximal graph.Keywords: Maximal graph, line graph, eulerian graph, comaximal graph -
Pages 13-29In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.Keywords: Second submodule, strongly cotop module, Zariski topology, spectral space
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Pages 31-39Let R be a commutative ring. In this paper we assert some properties of finitely generated comultiplication modules and Fitting ideals of them.Keywords: Fitting ideals, comultiplication module, simple module
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Pages 41-50In this paper we will generalize some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .Keywords: Tight closure_F?regular_weakly F?regular relative to a module
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Pages 51-61The rings considered in this article are commutative with identity 1≠0. By a proper ideal of a ring R, we mean an ideal I of R such that I≠R. We say that a proper ideal I of a ring R is a maximal non-prime ideal if I is not a prime ideal of R but any proper ideal A of R with I⊆A and I≠A is a prime ideal. That is, among all the proper ideals of R, I is maximal with respect to the property of being not a prime ideal. The concept of maximal non-maximal ideal and maximal non-primary ideal of a ring can be similarly defined. The aim of this article is to characterize ideals I of a ring R such that I is a maximal non-prime (respectively, a maximal non maximal, a maximal non-primary) ideal of R.Keywords: Maximal non, prime ideal, maximal non, maximal ideal, maximal non, primary ideal, maximal non, irreducible ideal
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Pages 63-72In this paper, we consider the finitely presented groups Gm and K(s,l) as follows;
Gm=⟨a,b|am=bm=1, [a,b]a=[a,b], [a,b]b=[a,b]⟩
K(s,l)=⟨a,b|abs=bla, bas=alb⟩;
and find the nth-commutativity degree for each of them. Also we study the concept of n-abelianity on these groups, where m,n,s and l are positive integers, m,n≥2 and g.c.d(s,l)=1.Keywords: Nilpotent groups, nth, commutativity degree, n, abelian groups