# Orders in power semigroups

## Author

**David Easdown** and **Victoria Gould**

## Status

Research Report 96-3

To appear in Glasgow Mathematical Journal

Date: December 1995

## Abstract

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

Secondary:

## Content

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1996-3.dvi (53kB)

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