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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homomorphisms of commutative cancellative semigroups into nonnegative real numbers


Authors: Mohan S. Putcha and Takayuki Tamura
Journal: Trans. Amer. Math. Soc. 221 (1976), 147-157
MSC: Primary 20M15
MathSciNet review: 0409700
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Abstract: Let S be a commutative cancellative semigroup and $ {T_0}$ be a cofinal subsemigroup of S. Let $ {h_0}$ be a homomorphism of $ {T_0}$ into the semigroup of nonnegative real numbers under addition. We prove that Kobayashi's condition [2] is necessary and sufficient for $ {h_0}$ to be extended to S. Further, we find a necessary and sufficient condition in order that the extension be unique. Related to this, the ``boundedness condition'' is introduced. For further study, several examples are given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0409700-1
PII: S 0002-9947(1976)0409700-1
Keywords: Commutative cancellative (idempotent-free) semigroup, cofinal subsemigroup, unitary subsemigroup, homomorphism, $ \mathcal{K}$-condition, $ \mathcal{B}$-condition (boundedness condition), unitary closure, filter, filter closure
Article copyright: © Copyright 1976 American Mathematical Society