Abstract
A subsemigroup S of a semigroup Q is a left (right) order in Q if every q is an element of Q can be written as q = a*b(q = ba*) for some a, b is an element of S, where a* denotes the inverse of a in a subgroup of Q and if, in addition, every square-cancellable element of S lies in a subgroup of Q. If S is both a left order and a right order in Q, we say that S is an order in Q. We show that if S is a left order in Q and S satisfies a permutation identity x(1)...x(n) = x(1 pi)...x(n pi) where 1 < 1 pi and n pi < n, then S and Q are commutative. We give a characterisation of commutative orders and decide the question of when one semigroup of quotients of a commutative semigroup is a homomorphic image of another. This enables us to show that certain semigroups have maximum and minimum semigroups of quotients. We give examples to show that this is not true in general.
| Original language | English |
|---|---|
| Pages (from-to) | 1201-1216 |
| Number of pages | 16 |
| Journal | Proceedings of the royal society of edinburgh section a-Mathematics |
| Volume | 126 |
| Publication status | Published - 1996 |
Keywords
- Algebra