E.L Lady

Nearly isomorphic torsion free abelian groups

Abstract Let K be the Krull-Schmidt-Grothendieck group for the category of finite rank torsion free abelian groups. The torsion subgroup T of K is determined and it is proved that K T is free. The investigation of T leads to the concept of near isomorphism, a new equivalence relation for finite rank torsion free abelian groups which is stronger than quasiisomorphism.

Summands of finite rank torsion free abelian groups

Abstract A finite rank torsion free abelian group has, up to isomorphism, only finitely many summands.

A Seminar on Splitting Rings for Torsion Free Modules over Dedekind Domains

This seminar is an introduction to the concepts dealt with in [10] through [15]. It is in some sense a “prequel” to those papers, since it provides most of the background material needed to read them. It is based on extensive talks given in a disjointed, disorganized fashion to varying audiences in Honolulu from time to time during the past few years.

Grothendieck rings for certain categories of quasihomomorphisms of torsion free modules over Dedekind domains

In this paper we consider the Krull-Schmidt-Grothendieck ring K(Q) for certain full subcategories Q of the category of quasihomomorphisms of finite rank torsion free modules over a Dedekind domain W. More specifically, we will be concerned with modules G such that W’ @ G is a Butler W’-module for some suitable finite integral extension W’ of W. We will usually also ‘assume that the typeset of W’ @ G consists of idempotent types. Let K = K(@‘) and let N = nil rad K. By a strongly indecomposable domain in Q, we mean a W-algebra D which is a commutative integral domain and such that the underlying W-module of D is strongly indecomposable and belongs to Q. If D is such a domain and G is any torsion free W-module, we let D-rank G = rank, Hom(G, D). We set P, = {[Cl [H] E K ] D-rank G = D-rank H}. We let E be the subring of K generated by all [D] such that D is a strongly indecomposable domain in 5F. Consider the following four properties: