Vol. 11, No. 5, 2018

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Rings isomorphic to their nontrivial subrings

Jacob Lojewski and Greg Oman

Vol. 11 (2018), No. 5, 877–883
Abstract

Let G be a nontrivial group, and assume that GH for every nontrivial subgroup H of G. It is a simple matter to prove that G or Gp for some prime p. In this note, we address the analogous (though harder) question for rings; that is, we find all nontrivial rings R for which RS for every nontrivial subring S of R.

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Keywords
direct sum, integral domain, polynomial ring, quotient field, reduced ring, zero divisor
Mathematical Subject Classification 2010
Primary: 16B99
Secondary: 20K99
Milestones
Received: 15 August 2017
Revised: 11 November 2017
Accepted: 20 November 2017
Published: 2 April 2018

Communicated by Scott T. Chapman
Authors
Jacob Lojewski
Department of Mathematics
University of Colorado
Colorado Springs, CO
United States
Greg Oman
Department of Mathematics
University of Colorado
Colorado Springs, CO
United States