Degree Type

Dissertation

Date of Award

1990

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Clifford Bergman

Abstract

A counterexample is given to show that not all quasivarieties of p-algebras lie between two consecutive varieties. It is shown that the quasivariety of p-algebras generated by the finite subdirectly irreducible p-algebras is the entire variety of p-algebras. Also, it is shown that this variety is not structurally complete and the class of its finitely subdirectly irreducible members coincides with the class of its subdirectly irreducible ones. This later result is used to show that there are no strict relatively congruence distributive quasivarieties of p-algebras. Relatively congruence distributive quasivarieties of Wajsberg algebras are characterized. The relative congruence extension property in the classes of p-algebras and Wajsberg algebras is studied. It is proved that in the first class only quasivarieties which are varieties possess this property. In the second one, it is shown that a quasivariety which is relatively congruence distributive or generates a proper subvariety has relative congruence extension property if and only if it is a variety.

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Hernando Gaitan

Language

en

Proquest ID

AAI9101351

File Format

application/pdf

File Size

99 pages

Included in

Mathematics Commons

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