Vol. 13, No. 5, 2020

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Rings whose subrings have an identity

Greg Oman and John Stroud

Vol. 13 (2020), No. 5, 823–828

Let R be a ring. A nonempty subset S of R is a subring of R if S is closed under negatives, addition, and multiplication. We determine the rings R for which every subring S of R has a multiplicative identity (which need not be the identity of R).

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absolutely algebraic field, Jacobson's theorem, reduced ring
Mathematical Subject Classification 2010
Primary: 16B99
Secondary: 13A99, 12E99
Received: 6 January 2020
Revised: 19 June 2020
Accepted: 6 August 2020
Published: 5 December 2020

Communicated by Kenneth S. Berenhaut
Greg Oman
Department of Mathematics
University of Colorado
Colorado Springs, CO
United States
John Stroud
Department of Physics
University of Colorado
Colorado Springs, CO
United States