Abstract
A subsemigroup S of a semigroup Q is a local left order in Q if, for every group R-class H of Q, S boolean AND H is a left order in H in the sense of group theory. That is, every q is an element of H can be written as a(#)b for some a, b S boolean AND H, where a(#) denotes the group inverse of a in H. On the other hand, S is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be written as c(#)d where c, d is an element of S and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. If one also insists that c and d can be chosen such that cRd in Q, then S is said to be a straight left order in Q.
This paper investigates the close relation between local left orders and straight left orders in a semigroup Q and gives some quite general conditions for a left order S in Q to be straight. In the light of the connection between locality and straightness we give a complete description of straight left orders that improves upon that in our earlier paper. (C) 2003 Elsevier Inc. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 514-541 |
| Number of pages | 28 |
| Journal | Journal of Algebra |
| Volume | 267 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 15 Sept 2003 |
Keywords
- group inverse
- semigroup of (left) quotients
- order
- straightness
- locality
- LEFT ORDERS