Rings whose subrings have an identity

Greg Oman; John Stroud

doi:10.2140/involve.2020.13.823

Abstract

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 $R$ ).

Citation

Download Citation

Greg Oman. John Stroud. "Rings whose subrings have an identity." Involve 13 (5) 823 - 828, 2020. https://doi.org/10.2140/involve.2020.13.823

Information

Received: 6 January 2020; Revised: 19 June 2020; Accepted: 6 August 2020; Published: 2020

First available in Project Euclid: 22 December 2020

MathSciNet: MR4190440

Digital Object Identifier: 10.2140/involve.2020.13.823

Subjects:

Primary: 16B99

Secondary: 12E99 , 13A99

Keywords: absolutely algebraic field , Jacobson's theorem , reduced ring

Abstract

Citation

Information

KEYWORDS/PHRASES

PUBLICATION TITLE:

PUBLICATION YEARS