2002/08/29 by Victoria Gould, Gould, Victoria
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #20M07 #Advanced Algebra and Logic #Chemical Synthesis and Analysis #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:20M07 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0208232
17 pages
arxiv created 2002/08/29 · openalex publication_date 2002/08/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.