Bulletin of the Australian Mathematical Society

Table of Contents - 1988 - Volume 38, Issue 02  

Research Article

On the lattice of right ideals of the endomorphism ring of an abelian group

Theodore G. Faticonia1

a1 Department of Mathematics, Fordham University, Bronx NY. 10458, United States of America.

Abstract

Let A be an abelian group, let xs2227 = End (A), and assume that A is a flat left xs2227-module. Then σ = { right ideals I xs2282 xs2227 | IA = A} generates a linear topology oil xs2227. We prove that Hom(A,·) is an equivalence from the category of those groups B xs2282 An satisfying B = Hom(A, B)A, onto the category of σ-closed submodules of finitely generated free right xs2227-modules. Applications classify the right ideal structure of A, and classify torsion-free groups A of finite rank which are (nearly) isomorphic to each A-generated subgroup of finite index in A.

(Received December 07 1987)