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Free algebras in locally finite semisimple varieties
by
Joel Berman
University of Illinois at Chicago
We consider the structure and cardinality of free objects in locally finite semisimple varieties of algebras. We provide upper bounds for the sizes of the finitely generated free algebras in such varieties and present various algebraic consequences that result when these upper bounds are obtained. These techniques are applied to some locally finite semisimple varieties that arise in algebraic logic and we thereby prove some new results and provide alternate proofs for some previously known theorems. Central to this work is the notion of a valuation f from a set X to an algebra A, which is any function f from X to A such that f(X) generates A. We analyze a variety V and its free algebra freely generated by a set X by studying the set of all valuations from X into finite algebras A in V that are subdirectly irreducible or belong to a set of generators of V.
Date received: May 23, 2008
Copyright © 2008 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 # caxi-11.