منابع مشابه
Grothendieck Groups of Abelian Group Rings
Let R be a noetherian ring, and G(R) the Grothendieck group of finitely generated modules over R. For a finite abelian group n, we describe G(Rn) as the direct sum of groups G(R’). Each R’ is the form RI<,,, I/n], where n is a positive integer and Cn a primitive nth root of unity. As an application, we describe the structure of the Grothendieck group of pairs (H. u), where His an abelian group ...
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Introduction. This survey is intended to introduce to logicians some notions, methods and theorems in set theory which arose—largely through the work of Saharon Shelah—out of (successful) attempts to solve problems in abelian group theory, principally the Whitehead problem and the closely related problem of the existence of almost free abelian groups. While Shelah’s first independence result re...
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While we were graduate students, Marty Isaacs and I worked together on the character theory of finite groups, studying in particular the character degrees of finite p-groups. Somewhat later, my interests turned to ring theory and infinite group theory. On the other hand, Marty continued with character theory and soon became a leader in the field. Indeed, he has had a superb career as a research...
متن کاملDivisibility 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...
متن کاملA note on decompositions in abelian group rings
We find a necessary and sufficient condition for a normal decomposition of the group of normed units in a commutative group ring (of prime characteristic) into certain its subgroups. This extends a recent assertion of ours in (Vladikavkaz Math. J., 2007). We also give some new proofs of own recent results published in (Miskolc Math. Notes,
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1986
ISSN: 0022-4049
DOI: 10.1016/0022-4049(86)90144-1