Vol. 99, No. 2, 1982

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Radical classes of regular rings with Artinian primitive images

Barry J. Gardner

Vol. 99 (1982), No. 2, 337–349

This paper deals with radical classes consisting of regular rings, all of whose primitive homomorphic images are artinian (such rings will be called PA-regular). Noteworthy examples of such radical classes include, for each n, the class of regular rings satisfying the condition

a nilpotent =⇒ an = 0,

and thus, in particular, the class of all strongly regular rings. It is shown that every radical class consisting of PA- regular rings is hereditary, and is the lower radical class defined by those of its members which are isomorphic to matrix rings of strongly regular rings with identities.

Mathematical Subject Classification
Primary: 16A21, 16A21
Received: 9 January 1980
Published: 1 April 1982
Barry J. Gardner