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Minimal varieties and quasivarieties

Part of: Algebraic structures Algebraic logic Varieties Other classes of algebra

Published online by Cambridge University Press:  09 April 2009

Clifford Bergman  and
Ralph McKenzie
Clifford Bergman
Affiliation:
Iowa State UniversityAmes, Iowa 50011, U.S.A.
Ralph McKenzie
Affiliation:
University of CaliforniaBerkeley, California 94720, U.S.A.
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Abstract

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We prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the sett of unary term perations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete.

Keywords

equationally complete varietyquasivarietycongruence modularclonestructurally complete logic.

MSC classification

Secondary: 08B15: Lattices of varieties 08C15: Quasivarieties 08B10: Congruence modularity, congruence distributivity 03G25: Other algebras related to logic 08A40: Operations, polynomials, primal algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 1 , February 1990 , pp. 133 - 147
Copyright
Copyright © Australian Mathematical Society 1990

References

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