J Austral Math Soc Ser A 46 pp177--183, 1989.

Lattices of Pseudovarieties

P. Agliano and J. B. Nation

Abstract

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 possitive universal sentence holding in all the lattices of subvarieties of varieties V(A) generated by algebras A Î P.

1980 AMS Subject Classification (1985 Revision): 08B15, 08C99

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Authors

P. Agliano

J. B. Nation

Department of Mathematics, University of Hawaii at Manoa, Honolulu, Hawaii 96822.