Lobachevskii Journal of Mathematics

, Volume 40, Issue 1, pp 60–66 | Cite as

Comparative and Allied UP-Filters

  • Y. B. JunEmail author
  • A. IampanEmail author


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, zX) (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 xX are provided.

Keywords and phrases

UP-algebra (implicative, comparative, allied) UP-filter 


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mathematics EducationGyeongsang National UniversityJinjuKorea
  2. 2.Department of Mathematics, School of ScienceUniversity of PhayaoPhayaoThailand

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