Semigroups of left quotients - the layered approach
| dc.creator | Gould, Victoria | |
| dc.date | 2002-08-29 | |
| dc.date.accessioned | 2026-07-07T04:50:27Z | |
| dc.date.available | 2026-07-07T04:50:27Z | |
| dc.description | 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# b where a and b are elements of 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 is related to b by Green's relation R in Q. A complete characterisation of straight left orders in terms of embeddable *-pairs is available. In this paper 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. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0208232 | |
| dc.identifier | http://arxiv.org/abs/math/0208232 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64799 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 20M07 | |
| dc.title | Semigroups of left quotients - the layered approach | |
| dc.type | text |