${R}_{0}$代数中的滤子格

Abstract In the present paper, some basic properties of MP filters of Ro algebra M are investigated. It is proved that（FMP（M）,包含,′∧^-∨^-,{1},M）is a bounded distributive lattice by introducing the negation operator ′, the meet operator ∧^-, the join operator ∨^- and the implicati on operator → on the set FMP（M） of all MP filters of M. Moreover, some conditions under which （FMP（M）,包含,′∨^-,→{1},M）is an Ro algebra are given. And the relationship between prime elements of FMP （M） and prime filters of M is studied. Finally, some equivalent characterizations of prime elements of .FMP （M） are obtained.

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

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.