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An embedding theorem with amalgamation for cancellative semigroups†
Published online by Cambridge University Press: 18 May 2009
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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).
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- 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
4Howie, J. M., Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511–534.CrossRefGoogle Scholar
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