强并半格中的C-滤子及其应用

吴洪博, 寇海燕

数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 287-300.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 287-300. DOI: 10.12386/A2015sxxb0028
论文

强并半格中的C-滤子及其应用

    吴洪博, 寇海燕
作者信息 +

C-Filters in Enriched Union Semi-Lattice with Its Applications

    Hong Bo WU, Hai Yan KOU
Author information +
文章历史 +

摘要

首先,在并半格中引入了上覆盖关系的概念以及由上覆盖关系确定的强并半格中的上覆盖概念,在强并半格中讨论了它们的基本性质;其次,通过上覆盖概念在强并半格中引入了C-滤子概念,证明了强并半格中的C-滤子是通常滤子,但强并半格中的通常滤子并非C-滤子;最后,研究了强并半格同态和余Frame同态之间的关系,证明了余Frame S与相应的CS-滤子型余Frame之间的同构定理.

Abstract

Firstly, the concept of upper covering relation in a union semi-lattice and upper coverage defined by the forme in an enriched union semi-lattice are introduced, the basic properties of them are discussed in enriched union semi-lattices. Secondly, the concept of C-filters is introduced in enriched union semi-lattices through upper coverage, it is proved that C-filters are usual filters, but usual filters are not C-filters in an enriched union semi-lattice. Thirdly, the relationships between morphisms of enriched union semi-lattice and co-Frames are investigated. At last, the isomorphism theorem between co-Frames and its CS-filter co-Frames is proved.

关键词

强并半格 / 上覆盖关系 / C-滤子 / 余Frame / 同构定理

Key words

enriched union semi-lattice / upper covering relation / C-filter / co-Frame / isomorphism theorem

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吴洪博, 寇海燕. 强并半格中的C-滤子及其应用. 数学学报, 2015, 58(2): 287-300 https://doi.org/10.12386/A2015sxxb0028
Hong Bo WU, Hai Yan KOU. C-Filters in Enriched Union Semi-Lattice with Its Applications. Acta Mathematica Sinica, Chinese Series, 2015, 58(2): 287-300 https://doi.org/10.12386/A2015sxxb0028

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基金

国家自然科学基金(11171196);中央高校基本科研业务费专项基金项目(GK201501001)

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