The Filter Lattices on ${R_{0}}$ Algebras
Received:December 07, 2006  Revised:March 08, 2008
Key Word: $R_{0}$ algebra   $MP$ filter   prime element   equivalent characterization.
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 Author Name Affiliation LUO Qing Jun Department of Mathematics, Xi'an Institute of Finance and Economics, Shaanxi 710061, China
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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.