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Subsemigroups of free products of semigroups

Published online by Cambridge University Press:  20 January 2009

James Renshaw
James Renshaw
Affiliation:
Faculty of Mathematical StudiesUniversity of SouthamptonSouthamptonSO9 5NH
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Abstract

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Given amalgams of semigroups [U; Ti] and [U;Si] with U⊆Ti⊆Si, it was proved by Howie in [6] that need not be embedded in . We use the homological techniques developed by Renshaw in [7, 9] and study three new conditions each of which imply the embeddability of the above free products.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 3 , October 1991 , pp. 337 - 357
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

REFERENCES

1.Bulman-Fleming, S. and McDowell, K., Absolutely flat semigroups, Pacific J. Math. 107 (1983), 319–333.CrossRefGoogle Scholar
2.Hall, T. E., Representation extension and amalgamation for semigroups, Quart. J. Math. Oxford (2) 29 (1978), 309–334.CrossRefGoogle Scholar
3.Hall, T. E., Generalised inverse semigroups and amalgamation, in Semigroups (Hall, T. E., Jones, P. R. and Preston, G. B., eds., Academic Press, New York, 1980), 145–157.CrossRefGoogle Scholar
4.Howie, J. M., An Introduction to Semigroup Theory (London Mathematical Society Monographs 7, Academic Press, London, 1976).Google Scholar
5.Howie, J. M., Epimorphisms and amalgamations: A survey of recent progress, Coll. Math. Soc. János Bolyai 39 (1981), 63–82.Google Scholar
6.Howie, J. M., Subsemigroups of amalgamated free products of semigroups, Proc. London Math. Soc. (3) 13 (1963), 672–686.CrossRefGoogle Scholar
7.Renshaw, J., Flatness and amalgamation in monoids, J. London Math. Soc. (2) 33 (1986), 73–88.CrossRefGoogle Scholar
8.Renshaw, J., Perfect amalgamation bases, J. Algebra, to appear.Google Scholar
9.Renshaw, J., Extension and amalgamation in monoids and semigroups, Proc. London Math. Soc. (3) 52 (1986), 119–141.CrossRefGoogle Scholar
10.Renshaw, J., Thesis (University of St. Andrews, 1985).Google Scholar