Comparative and Allied UP-Filters

초록

The notions of a comparative UP-filter and an allied UP-filter are introduced, and related properties are investigated. Relations between a UP-filter, an implicative UP-filter and a comparative UP-filter are discussed. Conditions for a UP-filter to be a comparative UP-filter are displayed. Conditions for a comparative UP-filter to be an implicative UP-filter are considered. We show that comparative UP-filters and implicative UP-filters coincide in a meet-commutative UP-algebra X satisfying the condition (for all x, y, z is an element of X) (x . (y . z) = y . (x . z)). Characterizations of a comparative UP-filter are stated. An extension property for comparative UP-filter is established. Conditions for a UP-filter to be an x-allied UP-filter for given x is an element of X are provided.

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