Maximal subsemilattices of the full transformation semigroup
type: Item
instance of: scholarly article
title: Maximal subsemilattices of the full transformation semigroup
zbMATH Open document ID: 0613.20042
DOI: 10.1007/BF02573107
published in: Semigroup Forum
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134873
review text: \textit{B. M. Schein} has posed the problem of determining the maximal subsemilattices of the full transformation semigroup T(X) on a finite set X. He has shown [Algebraic theory of semigroups, Szeged/Hung. 1976, Colloq. Math. Soc. János Bolyai 20, 519-544 (1979; Zbl 0405.08006)] that every subsemilattice S of T(X) induces, in a natural way, a partial order on X (called the transitivity order and denoted by TR(S)) which satisfies a number of conditions. Moreover S is completely determined by TR(S) together with the fixed point sets of S. The present authors look at the problem of determining precisely which of those partial orders on X determine maximal subsemilattices and they characterize these subsemilattices in the main results. This paper is a research announcement and consequently, contains no proofs. A paper with the same title, complete with proofs, has been submitted for publication.
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 3991789
zbMATH Keywords: maximal subsemilattices
zbMATH Keywords: full transformation semigroup
zbMATH Keywords: transitivity order
author: Michael Kunze
author: Siniša Crvenković
reviewed by: jun. Kenneth D. Magill
MaRDI profile type: Publication
cites work: Actions of semilattices
cites work: Q3853831
OpenAlex ID: W1992129495
description: scientific article; zbMATH DE number 3991789