Abstract
Margolis and Meakin use the Cayley graph of a group presentation to construct E-unitary inverse monoids [11]. This is the technique we refer to as graph expansion. In this paper we consider graph expansions of unipotent monoids, where a monoid is unipotent if it contains a unique idempotent. The monoids arising in this way are E-unitary and belong to the quasivariety of weakly left ample monoids. We give a number of examples of such monoids. We show that the least unipotent congruence on a weakly left ample monoid is given by the same formula as that for the least group congruence on an inverse monoid and we investigate the notion of proper for weakly left ample monoids.
Using graph expansions we construct a functor F-e from the category U of unipotent monoids to the category PWLA of proper weakly left ample monoids. The functor F-e is an expansion in the sense of Birget and Rhodes [2]. If we equip proper weakly left, ample monoids with an extra unary operation and denote the corresponding category by PWLA(0) then, regarded as a functor U --> PWLA(0), F-e is a left adjoint of the functor F-sigma :PWLA(0) --> U that takes a proper weakly left ample monoid to its greatest unipotent image.
Our main result uses the covering theorem of [8] to construct free weakly left ample monoids.
| Original language | English |
|---|---|
| Pages (from-to) | 447-463 |
| Number of pages | 17 |
| Journal | Communications in Algebra |
| Volume | 28 |
| Issue number | 1 |
| Publication status | Published - 2000 |
Keywords
- expansion
- ample
- unipotent
- SEMIGROUPS