Nilpotent elements in Grothendieck rings

Nilpotent Elements in Skew Polynomial Rings

 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...

On 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...

Extensions of Nilpotent P.P. Rings

Picard Groups, Grothendieck Rings, and Burnside Rings of Categories

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...

Schemic Grothendieck Rings I: Motivic Sites

We propose a suitable substitute for the classical Grothendieck ring of an algebraically closed field, in which any quasi-projective scheme is represented with its non-reduced structure. This yields a more subtle invariant, called the schemic Grothendieck ring. In order to include open subschemes and their complements, we introduce formal motives. Although originally cast in terms of definabili...