How many units can a commutative ring have?
Commutative Algebra
2017-01-11 v1 Group Theory
Rings and Algebras
Abstract
Laszlo Fuchs posed the following problem in 1960, which remains open: classify the abelian groups occurring as the group of all units in a commutative ring. In this note, we provide an elementary solution to a simpler, related problem: find all cardinal numbers occurring as the cardinality of the group of all units in a commutative ring. As a by-product, we obtain a solution to Fuchs' problem for the class of finite abelian -groups when is an odd prime.
Cite
@article{arxiv.1701.02341,
title = {How many units can a commutative ring have?},
author = {Sunil K. Chebolu and Keir Lockridge},
journal= {arXiv preprint arXiv:1701.02341},
year = {2017}
}
Comments
6 pages, to appear in Amer. Math. Monthly