The loop problem for Rees matrix semigroups

Abstract

We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zero-simple semigroups for which the loop problem is context-free. We also establish some results concerning loop problems for subsemigroups and Rees quotients.

Rees Matrix Constructions for Clustering of Data

“…Rees matrix semigroups and associated notions of completely 0-simple semigroups and Rees quotients are very well known in semigroup theory and play crucial roles in describing the structure of semigroups. See [20][21][22]34] for examples of recent results concerning these constructions.…”

“…We introduce a new type of multiple clustering systems, or clusterers, based on Rees matrix semigroups, which are well-known technical tools of semigroup theory (see [18]). Let us also refer, for example, to [21,22,34] for recent results concerning this construction. The class of all Brandt semigroups is a proper subclass of the class of all Rees matrix semigroups.…”