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Homomorphisms of Commutative Cancellative Semigroups into Nonnegative Real Numbers
Transactions of the American Mathematical Society
Let S be a commutative cancellative semigroup and Tq be a cofinal subsemigroup of S. Let Aq be a homomorphism of Tq into the semigroup of nonnegative real numbers under addition. We prove that Kobayashi's condition  is necessary and sufficient for h0 to be extended to 5. 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.doi:10.2307/1997545 fatcat:2eldp6zcljdw7i2st4uo76six4