Rings and covered groups

MTS 311 - Groups and Rings

Linear Groups and Group Rings

This paper consists of two parts. The first is concerned with free products in linear groups and uses the usual “ping pong” lemma and attractors to prove the results. What is new here is that we allow certain subspaces of V associated with the semisimple and generalized transvection operators to have dimensions larger than 1. The second part is concerned with applications of this machinery to i...

Sheaves of Groups and Rings

2 Abelian groups 5 2.1 Stalks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Sheaf Hom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Tensor products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Inverse and Direct Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

FA-presentable Groups and Rings

We consider structures which are FA-presentable. It is known that an FA-presentable finitely generated group is virtually abelian; we strengthen this result by showing that an arbitrary FA-presentable group is locally virtually abelian. As a consequence, we prove that any FA-presentable ring is locally finite; this is a significant restriction and allows us to say a great deal about the structu...

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...