Right Cancellative and Left Ample Monoids: Quasivarieties and Proper Covers
✍ Scribed by Victoria Gould
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 191 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
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 α → αα -1 . The idempotents of a left ample monoid form a semilattice and have a strong influence on the structure of 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 be a class of right cancellative monoids. A left ample monoid has a proper cover over if it has a proper cover with maximum right cancellative image in . We show that if is a quasivariety determined within right cancellative monoids by equations, then the left ample monoids having a proper cover over 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.