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 Kobayashiâs 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 âboundedness conditionâ is introduced. For further study, several examples are given.
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