Atlas home || Conferences | Abstracts | about Atlas

Algebras, Lattices, Varieties - A Conference in Honor of Walter Taylor
August 15-18, 2004
University of Colorado
Boulder, Colorado, USA

Organizers
Jennifer Hyndman, Keith Kearnes, Ralph McKenzie, George McNulty, Ágnes Szendrei, Ross Willard

View Abstracts
Conference Homepage

Varieties of Residuated Semilattices
by
Jeffrey Olson
University of Illinois at Chicago

The variety of hoops lies within CRS, the class of commutative, residuated, semi-lattice-ordered monoids. Hoops are "integral" in the sense that the monoid identity is greatest in the partial order. It is known that a variety of hoops is locally finite if and only if it is k-potent for some k < w, that is, it obeys xk » xk+1 (where concatenation indicates the monoid operation). We present Ck, a naturally-defined sub-class of CRS, whose integral members are exactly k-potent hoops. We show that the variety generated by Ck is locally finite. The result explains the local finiteness of k-potent hoops and other varieties of residuated structures, such as the negation-free subreducts of Sugihara monoids and representable idempotent commutative residuated lattices.

Date received: July 9, 2004

Copyright © 2004 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 # caoc-23.