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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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