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Title: Generating the full transformation semigroup using order preserving mappings
Authors: Higgins, PM
Mitchell, James David
Ruskuc, Nikola
Keywords: Ranks
QA Mathematics
Issue Date: Sep-2003
Citation: Higgins , P M , 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 .
Abstract: 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.
Version: Publisher PDF
Status: Peer reviewed
URI: http://hdl.handle.net/10023/1553
DOI: http://dx.doi.org/10.1017/S0017089503001460
ISSN: 0017-0895
Type: Journal article
Rights: (c)2003 Glasgow Mathematical Journal Trust
Appears in Collections:University of St Andrews Research
Mathematics & Statistics Research
Pure Mathematics Research



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