The Generalizations of Free Objects
by
Yow-Tzong Yeh
Massey University at Albany

Though the class of inverse semigroups is a variety, in general a class of regular semigroups is not a variety. A breakthrough was introduced by Hall and, independently, by Kadourek and Szendrei. They considered classes of regular semigroups closed under taking direct products, homomorphic images and regular subsemigroups, which they called e-varieties. Kadourek and Szendrei also introduced the concept of bifree object which plays a similar role as free object does for varieties. In 1992, Yeh showed that bifree objects exist in each e-variety of E-solid semigroups and in each e-variety of locally inverse semigroups but not beyond. In 1998, Churchill and Trotter further generalized the concept and introduced the concept of trifree object for e-varieties of locally E-solid semigroups. They also found a systematic way of generalizing the concept of n-free object to cover the entire lattice of e-varieties of regular semigroups.

Date received: June 7, 1998

Copyright © 1998 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 # cabd-38.