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Radical decompositions of idempotent algebras

Part of: Other classes of algebra Algebraic structures Semigroups

Published online by Cambridge University Press:  09 April 2009

B. J. Gardner
B. J. Gardner
Affiliation:
Mathematics Department University of TasmaniaG.P.O. Box 252C Hobart, Tasmania 7001, Australia
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Abstract

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A variant of Kurosh-Amitsur radical theory is developed for algebras with a collection of (finitary) operations ω, all of which are idempotent, that is satisfy the condition ω(x, x,…, x) = x. In such algebras, all classes of any congruence are subalgebras. In place of a largest normal radical subobject, a largest congruence with radical congruence classes is considered. In congruence-permutable varieties the parallels with conventional radical theory are most striking.

MSC classification

Secondary: 08A05: Structure theory 08C99: None of the above, but in this section 20M11: Radical theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 2 , April 1984 , pp. 213 - 236
Copyright
Copyright © Australian Mathematical Society 1984

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