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AAA61: 61st Workshop on General Algebra + 16th Conference of Young Algebraists
February 2-4, 2001
TU Darmstadt
Darmstadt, Germany

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A note on homomorphic images, subalgebras and various products
by
Boza Tasic
University of Waterloo, Waterloo, Canada

A note on homomorphic images, subalgebras and various products

A note on homomorphic images, subalgebras and various products

Boza Tasic
University of Waterloo, Canada

Abstract

Let I, H, S, P, Pfin, Pf, Pu, Ps be the usual operators on classes of algebras of the same type (P, Pfin, Pf, Pu, Ps are respectively for direct, finite , filtered, ultra and subdirect products). The partially ordered monoid generated by the operators H, S, P with respect to composition of operators, I as an identity element, and a natural ordering between operators is described by Pigozzi (Algebra Universalis 2 (1972), 346-353). The aim of this note is to summarize known results on the monoids of operators generated by some of the above introduced opearators.

In the case of H, S and one of the product opearators we have that <H, S, P>, <H, S, Pfin>, <H, S, Pf>, <H, S, Pu> are isomorphic 18 elements partially ordered monoids. <H, S, Ps> has 11 elements and it is actually lattice ordered monoid.

In case of H, S and two of the product operators the following results ts are known: <H, S, P, Ps> has 22 elements, <H, S, P, Pf> has 29 elements and <H, S, P, Pfin>, <H, S, Pu, Pf> have 44 elements.

Date received: January 26, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafo-65.