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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).

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

References

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