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Left orders in regular ℋ-Semigroups II

Published online by Cambridge University Press:  18 May 2009

Victoria Gould
Victoria Gould
Affiliation:
Department of Mathematics, University of York, Heslington, York Y015DD
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We make the convention that if a is an element of a semigroup Q then by writing a–1 it is implicit that a lies in a subgroup of Q and has inverse a–1 in this subgroup; equivalently, a ℋ a2 and a–1 is the inverse of a in Ha.

A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be written as a–1b where a, b ∈ S and, in addition, every element of S satisfying a weak cancellation condition which we call square-cancellable lies in a subgroup of Q. The notions of right order and semigroup of right quotients are defined dually; if S is both a left order and a right order in Q then S is an order in Q and Q is a semigroup of quotients of S.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 1 , January 1990 , pp. 95 - 108
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Bulman-Fleming, S. and McDowell, K., Absolutely flat semigroups, Pacific. J. Math. 107 (1983), 319–333.CrossRefGoogle Scholar
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Mathematical Surveys 7, Vols 1 and 2 (American Math. Soc, 1961).Google Scholar
3.Fountain, J. B., Abundant semigroups, Proc. London Math. Soc. (3) 44 (1982), 103–129.CrossRefGoogle Scholar
4.Fountain, J. B. and Petrich, M., Completely 0-simple semigroups of quotients, J. Algebra 101 (1986), 365–402.CrossRefGoogle Scholar
5.Fountain, J. B. and Petrich, M., Brandt semigroups of quotients, Math. Proc. Cambridge Philos. Soc. 98 (1985), 413–426.CrossRefGoogle Scholar
6.Fountain, J. B. and Petrich, M., Orders in normal bands of groups, in preparation.Google Scholar
7.Gould, V. A. R., Clifford semigroups of left quotients, Glasgow Math J. 28 (1986), 181–191.CrossRefGoogle Scholar
8.Gould, V. A. R., Orders in semigroups, Contributions to General Algebra 5 (Verlag Hölder-Pichler-Tempsky, 1987), 163–169.Google Scholar
9.Gould, V. A. R., Left orders in inverse ω-semigroups, Quart. J. Math. Oxford Ser. (2), to appear.Google Scholar
10.Gould, V. A. R., Absolutely flat completely O-simple semigroups of left quotients, J. Pure Appl. Algebra 55 (1988), 261–288.CrossRefGoogle Scholar
11.Gould, V. A. R., Left orders in regular ℋ-semigroups I, J. Algebra, to appear.Google Scholar
12.Howie, J. M., An introduction to semigroup theory (Academic Press, 1976).Google Scholar
13.Munn, W. D., Regular ω-semigroups, Glasgow Math. J. 9 (1968), 46–66.CrossRefGoogle Scholar