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Simple surjective algebras having no proper subalgebras

Part of: Varieties Algebraic structures

Published online by Cambridge University Press:  09 April 2009

Ágnes Szendrei
Ágnes Szendrei
Affiliation:
Bolyai InstituteAradi vértanúk tere 1 6720 Szeged, Hungary
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Abstract

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We prove that every finite, simple, surjective algebra having no proper subalgebras is either quasiprimal or affine or isomorphic to an algebra term equivalent to a matrix power of a unary permutational algebra. Consequently, it generates a minimal variety if and only if it is quasiprimal. We show also that a locally finite, minimal variety omitting type 1 is minimal as a quasivariety if and only if it has a unique subdirectly irreducible algebra.

MSC classification

Secondary: 08A05: Structure theory 08A40: Operations, polynomials, primal algebras 08B05: Equational logic, Mal′cev (Mal′tsev) conditions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 3 , June 1990 , pp. 434 - 454
Copyright
Copyright © Australian Mathematical Society 1990

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