Modules with only Finitely Many Direct Sum Decompositions up to Isomorphism

Abstract

In this paper we study almost Krull-Schmidt modules, that is, modules with only finitely many direct sum decompositions up to isomorphism. This is a finiteness con- dition on modules that has nothing to do with the other finiteness conditions usually considered in the mathematical literature, like being noetherian, or AB5 ⁄ , or having finite Goldie dimension, or finite dual Goldie dimension, or finite Krull dimension. Then we compute bounds on the number and the lengths of the direct sum decompositions of modules.