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On the natural ordering of -classes and of idempotents in a regular semigroup

Published online by Cambridge University Press:  18 May 2009

T. E. Hall
Affiliation:
Monash University, Clayton, Victoria, Australia, 3168
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In this paper we prove the following:

Let S be a regular semigroup anda, bany elements of S such that Jb = ≦ Ja. Then, for each idempotent e∈Ja, there exists an idempotent f∈ Jb such that f = ≦e.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Amer. Math. Soc, Math Surveys No. 7, Vols. I and II (Providence, R.I., 1961 and 1967).Google Scholar
2.Lallement, G. and Petrich, M., Some results concerning completely 0-simple semigroups, Bull. Amer. Math. Soc. 70 (1964) 777778.Google Scholar
3.Lallement, G., Demi-groupes reguliers (Doctoral dissertation), Ann. Mat. Pura. Appl. 77 (iv) (1967), 47130.Google Scholar
4.Preston, G. B., Matrix representations of inverse semigroups, J. Aust. Math. Soc. 9 (1969) 2961.CrossRefGoogle Scholar
5.Rhodes, J., Some results on finite semigroups, J. Algebra 4 (1966), 471504.CrossRefGoogle Scholar
6.Warne, R. J., Extensions of completely 0-simple semigroups by completely 0-simple semigroups, Proc. Amer. Math. Soc. 17 (1966), 524526.Google Scholar