English

Fuchs' problem for indecomposable abelian groups

Commutative Algebra 2015-05-14 v1 Group Theory

Abstract

More than 50 years ago, Laszlo 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.

Keywords

Cite

@article{arxiv.1505.03508,
  title  = {Fuchs' problem for indecomposable abelian groups},
  author = {Sunil K. Chebolu and Keir Lockridge},
  journal= {arXiv preprint arXiv:1505.03508},
  year   = {2015}
}

Comments

10 pages, accepted for publication in Journal of Algebra

R2 v1 2026-06-22T09:33:45.871Z