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The study of commutative semigroups with greatest group-homomorphism


Authors: Takayuki Tamura and Howard B. Hamilton
Journal: Trans. Amer. Math. Soc. 173 (1972), 401-419
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9947-1972-0315032-9
MathSciNet review: 0315032
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Abstract: This paper characterizes commutative semigroups which admit a greatest group-homomorphism in various ways. One of the important theorems is that a commutative semigroup $ S$ has a greatest group-homomorphic image if and only if for every $ a \in S$ there are $ b,c \in S$ such that $ abc = c$. Further the authors study a relationship between $ S$ and a certain cofinal subsemigroup and discuss the structure of commutative separative semigroups which have a greatest group-homomorphic image.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0315032-9
Keywords: Greatest group-homomorphism, cofinal unitary subsemigroup, group-congruence, gr-homomorphism, archimedean, greatest cancellative homomorphic image, greatest separative homomorphic image, semilattice of abelian groups, direct limit, local identity, cofinal cluster, archimedean components are $ \mathfrak{G}$-composed, $ \mathfrak{N}$-cluster, group-cluster, $ \mathcal{G}$-semigroup
Article copyright: © Copyright 1972 American Mathematical Society

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