#### 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
##### 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 $R$).

##### Keywords
absolutely algebraic field, Jacobson's theorem, reduced ring
##### Mathematical Subject Classification 2010
Primary: 16B99
Secondary: 13A99, 12E99