The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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FALLING SUBALGEBRAS AND IDEALS IN BH-ALGEBRAS

  • Kim, Eun-Mi (Department of Mathematics Education, Dongguk University) ;
  • Ahn, Sun-Shin (Department of Mathematics Education, Dongguk University)
  • Received : 2012.04.06
  • Accepted : 2012.06.25
  • Published : 2012.08.31
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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 $n$-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 $n$-fold strong ideal are stated. A relation between a fuzzy subalgebra/ideal and a falling subalgebra/ideal is provided.

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References

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