Abstract
The aim of this paper is to study certain quasivarieties of left ample monoids. Left ample monoids are monoids of partial one-one mappings of sets closed under the operation alpha bar right arrow alpha alpha(-1). The idempotents of a left ample monoid form a semilattice and have a strong influence on the structure BE the monoid; however, a left ample monoid need not be inverse. Every left ample monoid has a maximum right cancellative image and a proper cover which is also left ample. The structure of proper left ample monoids is well understood. Let Sr be a class of right cancellative monoids. A left ample monoid has a proper cover over V if it has a proper cover with maximum right cancellative image in V. We show that if Sr is a quasivariety determined within right cancellative monoids by equations, then the left ample monoids having a proper cover over V form a quasivariety. We achieve our aim using the technique of graph expansions to construct proper left ample monoids from presentations of right cancellative monoids. (C) 2000 Academic Press.
| Original language | English |
|---|---|
| Pages (from-to) | 428-456 |
| Number of pages | 29 |
| Journal | Journal of Algebra |
| Volume | 228 |
| Issue number | 2 |
| Publication status | Published - 15 Jun 2000 |
Keywords
- monoid
- right cancellative
- expansion
- left ample
- proper cover
- quasivariety
- SEMIGROUPS