• Title, Summary, Keyword: $\mathcal{N}$-subalgebras

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A COUPLED 𝒩-STRUCTURE WITH AN APPLICATION IN A SUBTRACTION ALGEBRA

  • Williams, D.R. Prince;Ahn, Sun Shin;Jun, Young Bae
    • Honam Mathematical Journal
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    • v.36 no.4
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    • pp.863-884
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    • 2014
  • In this paper, we introduce a coupled $\mathcal{N}$-structure which is the generalization of $\mathcal{N}$-structure. Using this coupled $\mathcal{N}$-structure, we have applied in a subtraction algebra and have introduced the notion of a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal. Also the characterization of coupled $\mathcal{N}$-ideal is presented.

N-SUBALGEBRAS OF TYPE (∈, ∈ ∨ q) BASED ON POINT N-STRUCTURES IN BCK/BCI-ALGEBRAS

  • Lee, Kyoung-Ja;Jun, Young-Bae;Zhang, Xiaohong
    • Communications of the Korean Mathematical Society
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    • v.27 no.3
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    • pp.431-439
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    • 2012
  • Characterizations of $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) are provided. The notion of $\mathcal{N}$-subalgebras of type ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) is introduced, and its characterizations are discussed. Conditions for an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) (resp. ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) to be an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}$) are considered.

ℵ-IDEALS OF BCK/BCI-ALGERBAS

  • Jun, Young Bae;Lee, Kyoung Ja;Song, Seok Zun
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.417-437
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    • 2009
  • 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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