Email this article Comparative and Allied UP-Filters
- Authors: Jun Y.B.1, Iampan A.2
-
Affiliations:
- Department of Mathematics Education
- Department of Mathematics, School of Science
- Issue: Vol 40, No 1 (2019)
- Pages: 60-66
- Section: Article
- URL: https://bakhtiniada.ru/1995-0802/article/view/203770
- DOI: https://doi.org/10.1134/S1995080219010086
- ID: 203770
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Abstract
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.
About the authors
Y. B. Jun
Department of Mathematics Education
Author for correspondence.
Email: skywine@gmail.com
Korea, Republic of, Jinju, 52828
A. Iampan
Department of Mathematics, School of Science
Author for correspondence.
Email: aiyared.ia@up.ac.th
Thailand, Phayao, 56000
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