ℵ-IDEALS OF BCK/BCI-ALGERBAS

  • Jun, Young Bae (Department of Mathematics Education (and RINS) Gyeongsang National University) ;
  • Lee, Kyoung Ja (Department of Mathematics Education Hannam University) ;
  • Song, Seok Zun (Department of Mathematics Cheju National University)
  • Received : 2009.05.26
  • Accepted : 2009.08.14
  • Published : 2009.09.30

Abstract

The notions of $\mathcal{N}$-subalgebras, (closed, commutative, retrenched) $\mathcal{N}$-ideals, $\theta$-negative functions, and $\alpha$-translations are introduced, and related properties are investigated. Characterizations of an $\mathcal{N}$-subalgebra and a (commutative) $\mathcal{N}$-ideal are given. Relations between an $\mathcal{N}$-subalgebra, an $\mathcal{N}$-ideal and commutative $\mathcal{N}$-ideal are discussed. We verify that every $\alpha$-translation of an $\mathcal{N}$-subalgebra (resp. $\mathcal{N}$-ideal) is a retrenched $\mathcal{N}$-subalgebra (resp. retrenched $\mathcal{N}$-ideal).

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