Vol. 30, No. 1, 1969

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On regular self-injective rings

Vasily Cateforis

Vol. 30 (1969), No. 1, 39–45

If R is a right non-singular ring (with 1) and Q is its (R. E. Johnson) maximal right quotient ring, then the R-epimorphism ipi qi piqi from (Q RQ)R to QR is not in general a monomorphism; in this paper we show that it is if, and only if, for each q Q,(R : q) = {r R|qr R} contains a finitely generated large right ideal of R. As a corollary to this we obtain: a (Von Neumann) regular ring R is right selfinjective if and only if every finitely generated nonsingular right R-module is projective.

Mathematical Subject Classification
Primary: 16.90
Received: 24 April 1968
Published: 1 July 1969
Vasily Cateforis