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 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 V be a class of right cancellative monoids. A left ample monoid has a proper cover overV if it has a proper cover with maximum right cancellative image in V. We show that if V 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.
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