Bulletin of the Belgian Mathematical Society - Simon Stevin

Structure of commutative cancellative subarchimedean semigroups

Antonio M. Cegarra and Mario Petrich

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Abstract

A commutative semigroup $S$ is subarchimedean if there is an element $z\in S$ such that for every $a\in S$ there exist a positive integer $n$ and $x\in S$ such that $z^n=ax$. Such a semigroup is archimedean if this holds for all ${z\in S}$. A commutative cancellative idempotent-free archimedean semigroup is an $\frak{N}$-semigroup. We study the structure of semigroups in the title as related to $\frak{N}$-semigroups.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 1 (2006), 101-111.

Dates
First available in Project Euclid: 19 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1148059336

Digital Object Identifier
doi:10.36045/bbms/1148059336

Mathematical Reviews number (MathSciNet)
MR2246114

Zentralblatt MATH identifier
1132.20037

Subjects
Primary: 20M14: Commutative semigroups 20M30: Representation of semigroups; actions of semigroups on sets

Keywords
semigroup commutative cancellative subarchimedean

Citation

Cegarra, Antonio M.; Petrich, Mario. Structure of commutative cancellative subarchimedean semigroups. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 1, 101--111. doi:10.36045/bbms/1148059336. https://projecteuclid.org/euclid.bbms/1148059336


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