### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*61*(2), 441-456.

**Commutative cancellative semigroups without idempotents.** / Hamilton, H. B.; Nordahl, Thomas E; Tamura, T.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 61, no. 2, pp. 441-456.

}

TY - JOUR

T1 - Commutative cancellative semigroups without idempotents

AU - Hamilton, H. B.

AU - Nordahl, Thomas E

AU - Tamura, T.

PY - 1975

Y1 - 1975

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84972573630&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972573630&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84972573630

VL - 61

SP - 441

EP - 456

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -