S-半群的完备化  

Completions of S-semigroups

作　　者：刘敏[1] 李玉林 LIU Min;LI Yu-lin(School of Sciences,Changan University,Xi'an 710064,Shaanxi,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《山东大学学报（理学版）》2022年第6期23-30,共8页Journal of Shandong University(Natural Science)

基　　金：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)。

摘　　要：引入S-半群的S-半群Quantale完备化的概念,证明S-半群_(S)A的所有S-半群Quantale完备化可以完全被_(S)A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。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 _(S)A can be fully characterized as compatible quotients of the power-set S-semigroup quantale corresponding to _(S)A.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.

关 键 词：序半群 QUANTALE S-半群 S-半群Quantale S-代数 

分 类 号：O153.1[理学—数学]