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Distributive Ockham algebras: free algebras and injectivity

Published online by Cambridge University Press:  17 April 2009

Moshe S. Goldberg
Moshe S. Goldberg
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia.
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Abstract

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This paper centres around the variety 0 of distributive Ockham algebras, and those subvarieties of 0 which are generated by a single finite subdirectly irreducible algebra A. We use H.A. Priestley's duality for bounded distributive lattices throughout. First, intrinsic descriptions of the duals of certain finite subdirectly irreducibles are given; these are later used to determine projectives in the dual categories. Next, left adjoints to the forgetful functors from 0 and Var(A) into bounded distributive lattices are obtained, thereby allowing us to describe all free algebras and coproducts of arbitrary algebras. Finally, by applying the duality, we characterize injectivity in Var(A) for each finite subdirectly irreducible algebra A.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 2 , October 1981 , pp. 161 - 203
Copyright
Copyright © Australian Mathematical Society 1981

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