Comparative and Allied UP-Filters
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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 (∀x, y, z ∈ 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 ∈ X are provided.
Keywords and phrasesUP-algebra (implicative, comparative, allied) UP-filter
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- 4.Y. B. Jun and A. Iampan, “Implicative UP–filters,” AfrikaMat. (submitted).Google Scholar