Abstract
A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be expressed as A where a(#)b E S and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. Here a(#) denotes the inverse of a in a subgroup of Q. We say that a left order S is straight in Q if in the above definition we can insist that a Rb in Q. A complete characterisation of straight left orders in terms of embeddable *-pairs is available. In this article we adopt a different approach, based on partial order decompositions of semigroups. Such decompositions include semilattice decompositions and decompositions of a semigroup into principal factors or principal *-factors. We determine when a semigroup that can be decomposed into straight left orders is itself a straight left order. This technique gives a unified approach to obtaining many of the early results on characterisations of straight left orders.
| Original language | English |
|---|---|
| Pages (from-to) | 167-185 |
| Number of pages | 19 |
| Journal | Communications in Algebra |
| Volume | 32 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2004 |
Keywords
- group inverse
- order
- partial order
- Quotients
- LEFT ORDERS