Vol. 76, No. 2, 1978

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ISSN: 0030-8730
Some radical properties of rings with (a,b,c) = (c,a,b)

David Pokrass

Vol. 76 (1978), No. 2, 479–483
Abstract

A ring is an s-ring if (for fixed s) As is an ideal whenever A is. We show that at least two different definitions for the prime radical are equivalent in s-rings. If R satisfies (a,b,c) = (c,a,b) then R is a 2-ring. In this note we investigate various properties of the prime and nil radicals of R. In addition, if R is a finite dimensional algebra over a field of characteristic 2 of 3 we show that the concepts of nil and nilpotent are equivalent.

Mathematical Subject Classification 2000
Primary: 17A30
Milestones
Received: 6 December 1976
Published: 1 June 1978
Authors
David Pokrass