Fuchs’ Problem for Indecomposable Abelian Groups

Authors

Sunil K. Chebolu, Illinois State UniversityFollow
Keir H. Lockridge, Gettysburg CollegeFollow

Document Type

Article

Publication Date

9-2015

Department 1

Mathematics

Abstract

More than 50 years ago, László Fuchs asked which abelian groups can be the group of units of a commutative ring. Though progress has been made, the question remains open. We provide an answer to this question in the case of indecomposable abelian groups by classifying the indecomposable abelian groups that are realizable as the group of units of a ring of any given characteristic.

Comments

Original version is available from the publisher, Elsevier.

DOI

10.1016/j.jalgebra.2015.05.011

Recommended Citation

Chebolu, Sunil K. and Lockridge, Keir. "Fuchs’ Problem for Indecomposable Abelian Groups." Journal of Algebra 438 (September 2015), 325-336.