Vol. 9, No. 3, 2016

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
When is a subgroup of a ring an ideal?

Sunil K. Chebolu and Christina L. Henry

Vol. 9 (2016), No. 3, 503–516
Abstract

Let R be a commutative ring. When is a subgroup of (R,+) an ideal of R? We investigate this problem for the rings d and i=1dni. In the cases of × and n × m, our results give, for any given subgroup of these rings, a computable criterion for the problem under consideration. We also compute the probability that a randomly chosen subgroup from n × m is an ideal.

Keywords
ring, subgroup, ideal, Mathieu subspace, Goursat
Mathematical Subject Classification 2010
Primary: 13Axx
Secondary: 20Kxx
Milestones
Received: 15 May 2015
Revised: 2 June 2015
Accepted: 17 June 2015
Published: 3 June 2016

Communicated by Kenneth S. Berenhaut
Authors
Sunil K. Chebolu
Department of Mathematics
Illinois State University
Normal, IL 61790
United States
Christina L. Henry
Department of Mathematics
Illinois State University
Normal, IL 61790
United States