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ISSN : 1226-0657

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Vol.19 No.3
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FALLING SUBALGEBRAS AND IDEALS IN BH-ALGEBRAS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.3, pp.251-262
https://doi.org/10.7468/jksmeb.2012.19.3.251
Kim, Eun-Mi
Ahn, Sun-Shin
Kim,, E. , & Ahn,, S. (2012). FALLING SUBALGEBRAS AND IDEALS IN BH-ALGEBRAS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(3), 251-262, https://doi.org/10.7468/jksmeb.2012.19.3.251
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Abstract

Based on the theory of a falling shadow which was first formulated by Wang([14]), a theoretical approach of the ideal structure in BH-algebras is established. The notions of a falling subalgebra, a falling ideal, a falling strong ideal, a falling <TEX>$n$</TEX>-fold strong ideal and a falling translation ideal of a BH-algebra are introduced. Some fundamental properties are investigated. Relations among a falling subalgebra, a falling ideal and a falling strong ideal, a falling <TEX>$n$</TEX>-fold strong ideal are stated. A relation between a fuzzy subalgebra/ideal and a falling subalgebra/ideal is provided.

keywords
falling shadow, (fuzzy, falling) subalgebra, (fuzzy, falling) strong ideal, (fuzzy, falling) <tex> $n$</tex>-fold strong ideal

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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