Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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
MathSciNet review: 0315032
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20M10

Retrieve articles in all journals with MSC: 20M10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0315032-9
PII: S 0002-9947(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