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 -