Vol. 10 No. 10 (2018): Subnexuses Based on ${\mathcal N}$-structures

Articles

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  Subnexuses Based on N-structures

  Morteza Norouzi, Ameneh Asadi, Young Bae Jun

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  Abstract

  The notion of a subnexus based on ${\mathcal{N}}$-function (briefly, ${\mathcal{N}}$-subnexus) is introduced, and related properties are investigated. Also, the notions of ${\mathcal{N}}$-subnexus of type $(\alpha, \beta)$, where $(\alpha, \beta)$ is $(\in, \in)$, $(\in, q)$, $(\in, \in\! \vee \, {q})$, $(q, \in)$, $(q,q)$, $(q, \in\! \vee \, {q})$, $(\overline{\in}, \overline{\in})$ and $(\overline{\in}, \overline{\in} \vee \overline{q})$, are introduced, and their basic properties are investigated. Conditions for an ${\mathcal{N}}$-structure to be an ${\mathcal{N}}$-subnexus of type $(q, \in\! \vee \, {q})$ are given, and characterizations of ${\mathcal{N}}$-subnexus of type $(\in, \in\! \vee \, {q})$ and $(\overline{\in}, \overline{\in} \vee \overline{q})$ are provided. Homomorphic image and preimage of ${\mathcal{N}}$-subnexus are discussed.

  References