On endoprimality of varieties
by
Kalle Kaarli
University of Tartu

An algebra A is endoprimal if its term functions are exactly the finitary functions on the universe of A that permute with all endomorphisms of A. A variety is endoprimal if so are all of its members. It is known that every primal algebra generates an endoprimal variety. Other known examples of endoprimal varieties are generated by certain finite Heyting algebras. The aim of the present work was to understand: Is the endoprimality of a finitely generated variety a rather rare feature or not? Since every variety contains a simple algebra we first tried to describe finite simple algebras generating endoprimal varieties. As a special case, we obtained a description of minimal endoprimal varieties.

Date received: April 29, 2008