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An embedding theorem with amalgamation for cancellative semigroups†

Published online by Cambridge University Press:  18 May 2009

J. M. Howie
J. M. Howie
Affiliation:
The University Glasgow
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Let {Si; i ε I} be a finite or infinite family of cancellative semigroups. Let U be a cancellative semigroup, and suppose that there exists, for each i in I, a monomorphism φi: u→ Si. We are interested in finding a semigroup T with the following properties.

(a) For each i in I, there is a monomorphism λi: Si → T such that uφiλi = uøjλi for all u ɛ U and all i, j in I. That is to say, there exists a monomorphism λ: U → T which equals øiλi for all i in I.

Siλi∩Sjλj = Uλ (i, j ε I; i ≠ j).

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 1 , January 1963 , pp. 19 - 26
Copyright
Copyright © Glasgow Mathematical Journal Trust 1963

References

REFERENCES

1Birkhoff, G., Lattice theory (Foreword on Algebra), Revised Edition, Amer. Math. Soc. Colloquium publications XXV (New York, 1948).Google Scholar
2Dubreil, P., Contribution à la théorie des demigroupes, Mem. Acad. Sci. Inst. France 63 (1941), no. 3, 1–52.Google Scholar
3Hall, M., The theory of groups, (New York, 1959).Google Scholar
4Howie, J. M., Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511–534.CrossRefGoogle Scholar
5Howie, J. M., Some problems in the theory of semigroups, Thesis, Oxford (1961).Google Scholar
6Kurosh, A. G., The theory of groups, vol. II, (New York, 1955), 29–32.Google Scholar
7Levi, F. W., On semigroups, Bull. Calcutta Math. Soc. 36 (1944), 141–146.Google Scholar