Abstract:

In order to establish the mathematical foundation of the intelligent information processing system and develop the logic algebraic theory itself, a new class of logic algebra——pseudo NM algebra has been proposed recently. This paper introduces and investigates the filter theory of pseudo NM algebra. The notions of filters，generated filters，normal filters and prime filters etc. are defined. Their basic properties are investigated, with the structures of generated filters obtained. We show that prime filters and irreducible filters are equivalent，and that maximum filters must be prime filters. The prime filter theorem of pseudo NM algebra and its some corollaries are established. All these results are the non-commutative generalizations of the corresponding ones of the filter theory of NM algebra.

Key words: NM algebra, filter, normal filter, prime filter