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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a theorem of Malcev


Author: Gérard Lallement
Journal: Proc. Amer. Math. Soc. 30 (1971), 49-54
MSC: Primary 20.93
DOI: https://doi.org/10.1090/S0002-9939-1971-0285646-8
MathSciNet review: 0285646
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Abstract: For any pair of distinct elements a, b in a finitely generated abelian semigroup S, we indicate what are the homomorphisms $ \phi $ of S onto a finite semigroup such that $ \phi (a) \ne \phi (b)$. This improves a previous result of Malcev which states that the considered semigroups are residually finite.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0285646-8
Keywords: Finitely generated abelian semigroup, residual finiteness, congruences of finite index, Green equivalence, Schützenberger group and representation
Article copyright: © Copyright 1971 American Mathematical Society