Semi-simple radical classes of algebras and attainability of identities

Barry J. Gardner

Vol. 61 (1975), No. 2, 401–416

DOI: 10.2140/pjm.1975.61.401

Abstract

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

Milestones

Received: 24 June 1975

Revised: 21 October 1975

Published: 1 December 1975