JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (6): 23-30.doi: 10.6040/j.issn.1671-9352.0.2021.566

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Completions of S-semigroups

LIU Min, LI Yu-lin   

  1. School of Sciences, Changan University, Xian 710064, Shaanxi, China
  • Published:2022-06-10

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Abstract: The concept of S-semigroup quantale completions for S-semigroups is introduced. It is proved that all S-semigroup quantale completions of an S-semigroup SA can be fully characterized as compatible quotients of the power-set S-semigroup quantale corresponding to SA. Three kinds of classical completion methods are given. Furthermore, S-algebra completions of double residuated S-semigroups are considered. The quotient with respect to the largest compatible nucleus on the down-set S-semigroup quantale is proved to be an S-algebra completion for an arbitrary double residuated S-semigroup.

Key words: partially ordered semigroup, Quantale, S-semigroup, S-semigroup quantale, S-algebra

CLC Number: 

  • O153.1
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