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Axioms 2018, 7(2), 26; https://doi.org/10.3390/axioms7020026

Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation Maps

1
Department of Mathematics, Jeju National University, Jeju 63243, Korea
2
Department of Mathematical Sciences, Shahid Beheshti University, Tehran 1983969411, Iran
3
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
*
Author to whom correspondence should be addressed.
Received: 4 February 2018 / Revised: 8 April 2018 / Accepted: 11 April 2018 / Published: 23 April 2018
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Abstract

Relations between I-quasi-valuation maps and ideals in B C K / B C I -algebras are investigated. Using the notion of an I-quasi-valuation map of a B C K / B C I -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 B C K / B C I -algebras are discussed. View Full-Text
Keywords: ideal; I-quasi-valuation map; I-valuation map; quasi-metric ideal; I-quasi-valuation map; I-valuation map; quasi-metric
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Song, S.-Z.; Bordbar, H.; Jun, Y.B. Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation Maps. Axioms 2018, 7, 26.

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