TY - JOUR
T1 - Generators and factorisations of transformation semigroups
AU - Higgins, PM
AU - Howie, John Mackintosh
AU - Ruskuc, Nikola
PY - 1998
Y1 - 1998
N2 - If E is the set of idempotents and G the group of units within a full transformation semigroup F-X. then EG = GE = F-X, if X is finite. The question of identifying the subsemigroup EG = GE = < G boolean OR E > in the case where X is infinite leads to an investigation of interrelations among various naturally occurring subsemigroups of F-X. In the final section it is shown that precisely two additional elements mu, nu are needed in order that G boolean OR E boolean OR {mu, nu} should generate F-X.
AB - If E is the set of idempotents and G the group of units within a full transformation semigroup F-X. then EG = GE = F-X, if X is finite. The question of identifying the subsemigroup EG = GE = < G boolean OR E > in the case where X is infinite leads to an investigation of interrelations among various naturally occurring subsemigroups of F-X. In the final section it is shown that precisely two additional elements mu, nu are needed in order that G boolean OR E boolean OR {mu, nu} should generate F-X.
KW - NATURAL PARTIAL ORDER
UR - http://www.scopus.com/inward/record.url?scp=33747035559&partnerID=8YFLogxK
U2 - 10.1017/S0308210500027360
DO - 10.1017/S0308210500027360
M3 - Article
SN - 0308-2105
VL - 128
SP - 1355
EP - 1368
JO - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
JF - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
IS - 6
ER -