Proper restriction semigroups - semidirect products and W-products

TY - JOUR

T1 - Proper restriction semigroups - semidirect products and W-products

AU - Gould, Victoria

AU - Szendrei, Maria

PY - 2013/10

Y1 - 2013/10

N2 - Fountain and Gomes [4] have shown that any proper left ample semigroup embeds into a so-called W-product, which is a subsemigroup of a reverse semidirect product T⋉Y of a semilattice Y by a monoid T, where the action of T on Y is injective with images of the action being order ideals of Y . Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim of this paper is to give necessary and sufficient conditions on a proper left restriction semigroup such that it embeds into a W-product. We also examine the complex relationship between W-products and semidirect products of the form Y⋊T .

AB - Fountain and Gomes [4] have shown that any proper left ample semigroup embeds into a so-called W-product, which is a subsemigroup of a reverse semidirect product T⋉Y of a semilattice Y by a monoid T, where the action of T on Y is injective with images of the action being order ideals of Y . Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim of this paper is to give necessary and sufficient conditions on a proper left restriction semigroup such that it embeds into a W-product. We also examine the complex relationship between W-products and semidirect products of the form Y⋊T .

U2 - 10.1007/s10474-013-0322-z

DO - 10.1007/s10474-013-0322-z

M3 - Article

SN - 1588-2632

VL - 141

SP - 36

EP - 57

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1-2

ER -