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Title:Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation Maps
Authors:Bordbar, Hashem (Author)
Jun, Young Bae (Author)
Song, Seok Zun (Author)
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Work type:Not categorized (r6)
Tipology:1.01 - Original Scientific Article
Organization:UNG - University of Nova Gorica
Abstract:Relations between I-quasi-valuation maps and ideals in BCK/BCI -algebras are investigated. Using the notion of an I-quasi-valuation map of a BCK/BCI-algebra, the quasi-metric space is induced, and several properties are investigated. Relations between the I-quasi-valuation map and the I-valuation map are considered, and conditions for an I-quasi-valuation map to be an I-valuation map are provided. A congruence relation is introduced by using the I-valuation map, and then the quotient structures are established and related properties are investigated. Isomorphic quotient BCK/BCI-algebras are discussed.
Keywords:ideal, I-quasi-valuation map, I-valuation map, quasi-metric
Year of publishing:2018
Number of pages:11
Numbering:7, 2
COBISS_ID:5491451 Link is opened in a new window
DOI:doi:10.3390/axioms7020026 Link is opened in a new window
License:CC BY 4.0
This work is available under this license: Creative Commons Attribution 4.0 International
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Year of publishing:2018