Homomorphisms of commutative cancellative semigroups into nonnegative real numbers
Mohan S. Putcha and Takayuki Tamura
Trans. Amer. Math. Soc. 221 (1976), 147-157
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Abstract: Let S be a commutative cancellative semigroup and be a cofinal subsemigroup of S. Let be a homomorphism of into the semigroup of nonnegative real numbers under addition. We prove that Kobayashi's condition  is necessary and sufficient for 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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Commutative cancellative (idempotent-free) semigroup,
-condition (boundedness condition),
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