Chinese Quarterly Journal of Mathematics ›› 2008, Vol. 23 ›› Issue (3): 442-445.

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On the Fractional Extensions in Commutative Ordered Semigroups 

  

  1. College of Science,Three Gorges University
  • Received:2005-04-05 Online:2008-09-30 Published:2023-09-25
  • About author: LUO Cong-wen(1965- ), male, native of Yichang, Hubei, a professor of Three Gorges University, Ph.D., engages in lattice theory.
  • Supported by:
     Supported by the Natural Science Foundation of Hubei Province in China(2004D006)

Abstract: In this paper we extend the construction of the field of rational numbers from the ring of integers to an arbitrary commutative ordered semigroup. We first construct a frac-tional ordered semigroup and a homomorphism φs : R → S-1R. Secondly, we characterize the commutative ordered semigroup so constructed by a universal mapping property.

Key words: ordered semigroup, fractional extension, homomorphism

CLC Number: