منابع مشابه
Divisibility Properties of Group Rings over Torsion-free Abelian Groups
Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...
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There is a great deal of literature on periodic rings, respectively, torsion-free rings (especially of rank two). The aim of this paper is to provide a link between these two topics. All groups considered here are Abelian, with addition as the group operation. By order of an element we always mean the additive order of this element. All rings are associative but not necessarily with identity. T...
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We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a unique automorphism mapping the first element onto the second one. We will show the existence of such a group of cardinality λ for any successor cardinal λ = μ+ with μ = μ0.
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We show, for each computable ordinal α and degree a > 0(α), the existence of a torsion-free abelian group with proper αth jump degree a.
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Suppose that G is an abelian p-separable group and R is a commutative unital ring of prime characteristic p. It is proved that if Rp i possesses nilpotent elements for each natural number i, then the normalized Sylow p-subgroup S(RG) in the group ring RG is torsion-complete if and only if G is p-bounded. This supplies our recent results from Acta Math. Hung. (1997), Ric. Mat. (2002), Tamkang J....
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ژورنال
عنوان ژورنال: Bulletin of the Faculty of Science, Ibaraki University. Series A, Mathematics
سال: 1993
ISSN: 1883-4345,0579-3068
DOI: 10.5036/bfsiu1968.25.11