Quasivarieties of idempotent semigroups
by
M.E. Adams
State University of New York at New Paltz
Coauthors: W. Dziobiak (University of Puerto Rico at Mayagüez)

A quasivariety K of algebras of finite type is said to be Q-universal if, for any quasivariety M of finite type, L(M) is a homomorphic image of a sublattice of L(K), where L(M) and L(K) are the lattices of quasivarieties contained in M and K, respectively.

It is shown that the varieties LSN of all left semi-normal idempotent semigroups and RSN all right semi-normal idempotent semigroups are Q-universal. It follows that a free lattice on \omega generators may be embedded in each of L(LSN) and L(RSN). In particular, L(LSN) and L(RSN) each fail to satisfy any non-trivial lattice identity.

Date received: January 1, 2002

Copyright © 2002 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 # caig-45.