${R}_{0}$代数中的滤子格

The Filter Lattices on ${R_{0}}$ Algebras

中文关键词:  $R_{0}$代数  MP滤子  素元  等价刻画.

英文关键词:$R_{0}$ algebra  $MP$ filter  prime element  equivalent characterization.

中文摘要:

      本文研究了$R_{0}$代数$M$中MP滤子的基本性质.通过在$M$的全体MP滤子之集${\cal F}_{MP}(M)$中引入$',\bar\wedge,\bar\vee$和$\Longrightarrow$运算,证明了$({{{\cal F}}_{MP}}(M),\subset,\bar\wedge,\bar\vee,\{1\},M)$是有界分配格,同时给出了$({{{\cal F}}_{MP}}(M),\subset,',\bar\vee,\Longrightarrow,\{1\},M)$成为$R_

英文摘要:

      In the present paper, some basic properties of $MP$ filters of $R_{0}$ algebra $M$ are investigated. It is proved that $({\cal F}_{MP}(M),\subset,',\bar\wedge,\bar\vee,\{1\},M)$ is a bounded distributive lattice by introducing the negation operator $'$, the meet operator $\bar\wedge$, the join operator $\bar\vee$ and the implication operator $\Longrightarrow$ on the set ${\cal F}_{MP}(M)$ of all $MP$ filters of $M$. Moreover, some conditions under which $({\cal F}_{MP}(M),\subset,',\bar\vee,\Longrightarrow,\{1\},M)$ is an $R_{0}$ algebra are given. And the relationship between prime elements of ${\cal F}_{MP}(M)$ and prime filters of $M$ is studied. Finally, some equivalent characterizations of prime elements of ${\cal F}_{MP}(M)$ are obtained.