Commutative cancellative semigroups without idempotents

H. B. Hamilton, Thomas E Nordahl, T. Tamura

Research output: Contribution to journal › Article

9 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)441-456
Number of pages16
JournalPacific Journal of Mathematics
Volume61
Issue number2
StatePublished - 1975
Externally publishedYes

Fingerprint

Idempotent
Semigroup
Free Semigroup
Finite Rank
Homomorphism
Abelian group
Non-negative
Integer

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Pacific Journal of Mathematics, Vol. 61, No. 2, 1975, p. 441-456.

Research output: Contribution to journal › Article

Hamilton, HB, Nordahl, TE & Tamura, T 1975, 'Commutative cancellative semigroups without idempotents', Pacific Journal of Mathematics, vol. 61, no. 2, pp. 441-456.
Hamilton HB, Nordahl TE, Tamura T. Commutative cancellative semigroups without idempotents. Pacific Journal of Mathematics. 1975;61(2):441-456.
Hamilton, H. B. ; Nordahl, Thomas E ; Tamura, T. / Commutative cancellative semigroups without idempotents. In: Pacific Journal of Mathematics. 1975 ; Vol. 61, No. 2. pp. 441-456.
@article{a497170fc2aa447f8a2e5aa7bfc950ca,
title = "Commutative cancellative semigroups without idempotents",
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.",
author = "Hamilton, {H. B.} and Nordahl, {Thomas E} and T. Tamura",
year = "1975",
language = "English (US)",
volume = "61",
pages = "441--456",
journal = "Pacific Journal of Mathematics",
issn = "0030-8730",
publisher = "University of California, Berkeley",
number = "2",

}

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 -

Access to Document