Vol. 56, No. 2, 1975

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Regularity and quotients in rings with involution

Charles Philip Lanski

Vol. 56 (1975), No. 2, 565–574

Let R be a ring with involution. There exists a unique maximal nilpotent -ideal N of R such that R∕N with the induced involution satisfies the property that any regular element ot S, the subring generated by the symmetric elements of R∕N is regular in R∕N. When N = 0 we say that R satisfies the regularity condition. Assuming this condition, (Q(R)) = R if and only if Q(S) = S. The existence of Q(S) implies the existence of Q(R), and the converse is shown in some special cases. If either S is commutative or R is a semi-prime Goldie ring, then the relation between Q(R) and Q(S) is explicitly described.

Mathematical Subject Classification
Primary: 16A28
Received: 26 November 1973
Published: 1 February 1975
Charles Philip Lanski