Orders in power semigroups


David Easdown and Victoria Gould


Research Report 96-3
To appear in Glasgow Mathematical Journal
Date: December 1995


We consider the Fountain-Petrich notion of a semigroup of quotients. If Q is a semigroup of quotients of S we also say that S is an order in Q. We concentrate here on orders in the restricted power semigroup P(Q) of a semigroup Q, where P(Q) consists of all non-empty finite subsets of Q under the natural multiplication. Our first result shows that if S is a commutative cancellative semigroup with group of quotients G, then P(S) is an order in P(G). In the latter part of the paper we give necessary and sufficient conditions for P(S) to be an order in P(Q), where Q is a semilattice of torsion-free commutative groups and S is an order in Q.

Key phrases

semigroups of quotients. restricted power semigroups. semilattices of torsion free abelian groups.

AMS Subject Classification (1991)

Primary: 20M10 20M14


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