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Homomorphisms of commutative cancellative semigroups into nonnegative real numbers
1976
Transactions of the American Mathematical Society
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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 [2] 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:10.1090/s0002-9947-1976-0409700-1
fatcat:cjk5tpquyfdfrar7r3i7ntmmoq