On the Representation of Monoids by O-Endomorphisms of linearly ordered Sets
by
Vladimir Repnitskii
Ural State University, Ekaterinburg, Russia
Coauthors: Alexei Vernitskii (University of Middlesex)

A mapping \alpha of a linearly ordered set C into C is called an o-endomorphism if p <= q implies p \alpha <= q \alpha for any p, q in C. The set of all o-endomorphisms of C forms a monoid E(C) under multiplication of mappings. We examine necessary and sufficient conditions in order for a monoid to embed into the monoid E(C) for a suitable linearly ordered set C. In particular, we charactirize monoids representable by o-endomorphisms of a finite linearly ordered set in terms of quasi-identities. As a corollary, we obtain necessary and sufficient conditions in order for a group to embed in the group of all o-automorphisms of a linearly ordered set.

Date received: May 18, 2000

Copyright © 2000 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 # caee-41.