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Almost strongly unital rings

Greg Oman and Evan Senkoff

Vol. 16 (2023), No. 3, 453–465
Abstract

Recently Oman and Stroud (Involve 13:5 (2020), 823–828) determined all rings R for which every subring of R has an identity (which need not be the identity of R), calling such rings strongly unital. We extend this work to determine the rings S for which every proper subring of S has an identity, yet S does not, calling such rings almost strongly unital. We conclude by classifying the rings T for which a subring R of T has an identity if and only if there is a subring S of T such that R S T.

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Keywords
Artinian ring, commutative ring, nilpotent element, reduced ring, strongly unital ring
Mathematical Subject Classification
Primary: 13A99
Secondary: 13M99, 13E10
Milestones
Received: 22 January 2022
Revised: 19 July 2022
Accepted: 19 July 2022
Published: 10 August 2023

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