Vol. 67, No. 1, 1976

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v-prehomomorphisms on inverse semigroups

D. B. McAlister

Vol. 67 (1976), No. 1, 215–231

A mapping 𝜃 of an inverse semigroup S into an inverse semigroup T is called a v-prehomomorphism if, for each a,b S, (ab)𝜃 a𝜃b𝜃 and (a1)𝜃 = (a𝜃)1. The congruences on an E-unitary inverse semigroup P(G,𝒳,𝒴) are determined by the normal partition of the idempotents, which they induce, and by v-prehomorphisms of S into the inverse semigroup of cosets of G.

Inverse semigroups, with v-prehomomorphisms as morphisms, constitute a category containing the category of inverse semigroups, and homomorphisms, as a coreflective subcategory. The coreflective map η : S V (S) is an isomorphism if the idempotents of S form a chain and the converse holds if S is E-unitary or a semilattice of groups. Explicit constructions are given for all v-prehomomorphisms on S in case S is either a semilattice of groups or is bisimple.

Mathematical Subject Classification 2000
Primary: 20M15
Received: 24 May 1976
Published: 1 November 1976
D. B. McAlister