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Lattices of pseudovarieties

Part of: Varieties Other classes of algebra

Published online by Cambridge University Press:  09 April 2009

P. Agliano  and
J. B. Nation
P. Agliano
Affiliation:
Department of Mathematics, University of Hawaii at Manoa, Honolulu Hawaii 96822
J. B. Nation
Affiliation:
Department of Mathematics, University of Hawaii at Manoa, Honolulu Hawaii 96822
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Abstract

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We consider the lattice of pseudovarieties contained in a given pseudovariety P. It is shown that if the lattice L of subpseudovarieties of P has finite height, then L is isomorphic to the lattice of subvarieties of a locally finite variety. Thus not every finite lattice is isomorphic to a lattice of subpseudovarieties. Moreover, the lattice of subpseudovarieties of P satisfies every positive universal sentence holding in all lattice of subvarieties of varieties V(A) ganarated by algebras A ε P.

MSC classification

Secondary: 08B15: Lattices of varieties 08C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 177 - 183
Copyright
Copyright © Australian Mathematical Society 1989

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