S-半群的完备化

doi:10.6040/j.issn.1671-9352.0.2021.566

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (6): 23-30.doi: 10.6040/j.issn.1671-9352.0.2021.566

• • 上一篇

S-半群的完备化

刘敏,李玉林

长安大学理学院, 陕西西安 710064

发布日期:2022-06-10
作者简介:刘敏(1984— ),男,博士,副教授,研究方向为格上拓扑学. E-mail:liumin@chd.edu.cn
基金资助:
国家自然科学基金资助项目(11871320);陕西省自然科学基础研究计划(2022JM-032)

Completions of S-semigroups

LIU Min, LI Yu-lin

School of Sciences, Changan University, Xian 710064, Shaanxi, China

Published:2022-06-10

摘要/Abstract

摘要： 引入S-半群的S-半群Quantale完备化的概念,证明S-半群_SA的所有S-半群Quantale完备化可以完全被_SA对应的幂集S-半群Quantale的相容商所刻画,给出了3种典型的完备化方法。此外,研究了双重剩余S-半群的S-代数完备化,证明了下集S-半群Quantale上最大相容核映射的商是任意双重剩余S-半群的S-代数完备化。

关键词: 序半群, Quantale, S-半群, S-半群Quantale, S-代数

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

中图分类号:

O153.1

刘敏,李玉林. S-半群的完备化[J]. 《山东大学学报(理学版)》, 2022, 57(6): 23-30.

LIU Min, LI Yu-lin. Completions of S-semigroups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(6): 23-30.

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S-半群的完备化

Completions of S-semigroups

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