Vol. 61, No. 2, 1975

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Semi-simple radical classes of algebras and attainability of identities

Barry J. Gardner

Vol. 61 (1975), No. 2, 401–416

This paper is concerned with the investigation of some interplay between the theories of (Kurosh-Amitsur) radicals and varieties of (not necessarily associative) algebras. Specifically, it is shown that a variety is a radical class if and only if it is closed under extensions, while a radical class which is also a semi-simple class is the same thing as a variety with attainable identities in the sense of T. Tamura (J. Algebra 3 (1966), 261–276). In certain instances it is shown that the two properties of varieties are equivalent.

Mathematical Subject Classification 2000
Primary: 17A99
Secondary: 16A21
Received: 24 June 1975
Revised: 21 October 1975
Published: 1 December 1975
Barry J. Gardner