Vol. 57, No. 1, 1975

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On a theorem of Brauer-Cartan-Hua type

Israel (Yitzchak) Nathan Herstein

Vol. 57 (1975), No. 1, 177–181

We shall be concerned here with the nature of subrings of a ring with involution which are invariant with respect to certain combinations of elements. To be more precise, let R be a ring with involution and suppose that A is a subring of R such that xAxA for all x R. Can we say something definitive about the structure of A? We shall see that if R is semi-prime then we do get a dichotomy of the Brauer-Cartan-Hua type, namely, A must contain a nonzero ideal of R or A must be central.

Mathematical Subject Classification
Primary: 16A28
Received: 19 June 1974
Published: 1 March 1975
Israel (Yitzchak) Nathan Herstein