Generating the full transformation semigroup using order preserving mappings
Date
09/2003Metadata
Show full item recordAbstract
For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappings O-X on X modulo the full transformation semigroup Ex. In other words, we ask what is the smallest cardinality of a set A of mappings such that <O-X boolean OR A> = T-X. When X is countably infinite or well-ordered (of arbitrary cardinality) we show that this number is one, while when X = R (the set of real numbers) it is uncountable.
Citation
Higgins , PM , Mitchell , J D & Ruskuc , N 2003 , ' Generating the full transformation semigroup using order preserving mappings ' , Glasgow Mathematical Journal , vol. 45 , no. 3 , pp. 557-566 . https://doi.org/10.1017/S0017089503001460
Publication
Glasgow Mathematical Journal
Status
Peer reviewed
ISSN
0017-0895Type
Journal article
Rights
(c)2003 Glasgow Mathematical Journal Trust
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.