### Abstract

A commutative cancellative idempotent-free semigroup (CCIF-) S can be described in terms of a commutative cancellative semigroup C with identity, an ideal of C, and a function of C × C into integers. If C is an abelian group, S has an archimedean component as an ideal; S is called an ℜ-semigroup. A CCIF-semigroup of finite rank has nontrivial homomorphism into nonnegative real numbers.

Original language | English (US) |
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Pages (from-to) | 441-456 |

Number of pages | 16 |

Journal | Pacific Journal of Mathematics |

Volume | 61 |

Issue number | 2 |

State | Published - 1975 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Hamilton, H. B., Nordahl, T. E., & Tamura, T. (1975). Commutative cancellative semigroups without idempotents.

*Pacific Journal of Mathematics*,*61*(2), 441-456.