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The natural partial order on an abundant semigroup

Published online by Cambridge University Press:  20 January 2009

Mark V. Lawson
Mark V. Lawson
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD
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In this paper we will study the properties of a natural partial order which may bedefined on an arbitrary abundant semigroup: in the case of regular semigroups werecapture the order introduced by Nambooripad [24]. For abelian PP rings our order coincides with a relation introduced by Sussman [25], Abian [1, 2] and further studied by Chacron [7]. Burmistroviˇ [6] investigated Sussman's order on separative semigroups. In the abundant case his order coincides with ours: some order theoretic properties of such semigroups may be found in a paper by Burgess [5].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 2 , June 1987 , pp. 169 - 186
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

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