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Orders in power semigroups

Published online by Cambridge University Press:  18 May 2009

David Easdown  and
Victoria Gould
David Easdown
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
Victoria Gould
Affiliation:
Department of Mathematics, University of York, Heslington, York Y01 5DD, England
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In this paper we consider examples of orders in restricted power semigroups, where for any semigroup Sthe restricted power semigroup is given by with multiplication XY = {xy:x ∈ X, y ∈ Y} for all X, Y ∈ . We use the notion of order introduced by Fountain and Petrich in [2] which first appears in the form used here in [3]. If S is a subsemigroup of Q then S is an order in Q and Q is a semigroup of quotients of S if any q ∈ Q can be written as q = a*b = cd* where a, b, c, d ∈ S is the inverse of a(d) in a subgroup of Q, and in addition, all elements of S satisfying a weak cancellability condition called square-cancellability lie in a subgroup of Q.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996 , pp. 39 - 47
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

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