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Subnexuses Based on N-structures

Authors

Morteza Norouzi Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord
Ameneh Asadi Department of Mathematics, Payame Noor University, Tehran, Iran.
Young Bae Jun Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

DOI:

https://doi.org/10.52737/18291163-2018.10.10-1-15

Keywords:

Nexus, subnexus, $\mathcal{N}$-structure, $q$-support, $\in \vee {q}$-support}

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.