Logo image
Back
Agreeable semigroups
Journal article   Peer reviewed

Agreeable semigroups

M. Jackson and T. Stokes
Journal of Algebra, Vol.266(2), pp.393-417
2003
DOI: https://doi.org/10.1016/S0021-8693(03)00314-4
url
Free to Read *No subscription requiredView

Abstract

This paper concerns the theory of partial maps under composition and more generally, the RC-semigroups introduced by Jackson and Stokes [Semigroup Forum 62 (2001) 279–310] (semigroups with a unary operation called (right) closure). Many of the motivating examples have a natural meet-semilattice structure; the inverse semigroup of all injective partial transformations of a set and the semigroup of all binary operations under composition are two examples. We here view the semilattice meet as an additional operation, thereby obtaining a variety of algebras with one unary and two binary operations. The two non-semigroup operations are then shown to be captured by a single binary operation, via the notion of an agreeable semigroup. We look at a number of properties of these structures including their congruences (which are uniquely determined by their restriction to certain idempotents), a relationship with so-called interior semigroups, and a natural category associated with a large variety of RC-semigroups (which includes all inverse semigroups). For example, we show that the existence of equalisers in this category is intimately connected with the existence of the natural meet-semilattice structure.

Details

Metrics

63 Record Views
23 Times Cited - Web of Science

InCites Highlights

These are selected metrics from InCites Benchmarking & Analytics tool, related to this output

Collaboration types
Domestic collaboration
Citation topics
9 Mathematics
9.280 Algebra & Topology
9.280.1047 Algebraic Logic
Web Of Science research areas
Mathematics
ESI research areas
Mathematics
Logo image