Subrings which are closed with respect to taking the inverse

Szigeti, Jenő and van Wyk, Leon (2007) Subrings which are closed with respect to taking the inverse. JOURNAL OF ALGEBRA, 318 (2). pp. 1068-1076. ISSN 0021-8693

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Abstract

Let S be a subring of the ring R. We investigate the question of whether S ∩ U(R) = U(S) holds for the units. In many situations our answer is positive. There is a special emphasis on the case when R is a full matrix ring and S is a structural subring of R defined by a reflexive and transitive relation.

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