Homomorphisms of commutative cancellative semigroups into nonnegative real numbers
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- by Mohan S. Putcha and Takayuki Tamura PDF
- Trans. Amer. Math. Soc. 221 (1976), 147-157 Request permission
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.References
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- Yuji Kobayashi, Homomorphisms on $N$-semigroups into $R_{+}$ and the structure of $N$-semigroups, J. Math. Tokushima Univ. 7 (1973), 1–20. MR 325484
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 221 (1976), 147-157
- MSC: Primary 20M15
- DOI: https://doi.org/10.1090/S0002-9947-1976-0409700-1
- MathSciNet review: 0409700