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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We discuss the Picard group, the Grothendieck ring, and the Burnside ring of a symmetric monoidal category, and we consider examples from algebra, homological algebra, topology, and algebraic geometry. In October, 1999, a small conference was held at the University of Chicago in honor of Saunders Mac Lane’s 90th birthday. I gave a talk there based on a paper that I happened to have started writ...
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We will calculate completely the Grothendieck rings, in the sense of first order logic, of o-minimal expansions of ordered abelian groups by introducing the notion of the bounded Euler characteristic.
متن کاملOn Relative Grothendieck Rings
Let K be a field of characteristic pi^O, to exclude trivial cases) and let G be a finite goup. A XG-module M is a finite dimensional K-vector space, on which G acts Jf-linearly from the left. The Green ring a(G) of G(w.r.t. K) is the free abelian group, spanned by the isomorphism classes of indecomposable i£G-modules, with the multiplication induced from the tensor product © x of KGmodules (see...
متن کاملInduction and Structure Theorems for Grothendieck and Witt Rings of Orthogonal Representations of Finite Groups
The Grothendieckand Wittring of orthogonal representations of a finite group is defined and studied. The main application (only indicated) is the reduction of the computation of Wall's various L-groups for a finite group n to those subgroups of n, which are a semidirect product of a cyclic group y of odd order with a 2-group /?, such that any element in ft acts on y either by the identity or by...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.2307/2048122