TY - JOUR
T1 - Generating the full transformation semigroup using order preserving mappings
AU - Higgins, PM
AU - Mitchell, James David
AU - Ruskuc, Nikola
PY - 2003/9
Y1 - 2003/9
N2 - 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 = 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.
AB - 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 = 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.
KW - Ranks
UR - http://www.scopus.com/inward/record.url?scp=0141640991&partnerID=8YFLogxK
U2 - 10.1017/S0017089503001460
DO - 10.1017/S0017089503001460
M3 - Article
SN - 0017-0895
VL - 45
SP - 557
EP - 566
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
IS - 3
ER -