α-Ideals in Bounded Commutative Residuated Lattices-Reference-Cited by-同舟云学术

α-Ideals in Bounded Commutative Residuated Lattices

Published:2022-10-11 Issue: Volume: Page:1-20
ISSN:1793-0057
Container-title:New Mathematics and Natural Computation
language:en
Short-container-title:New Math. and Nat. Computation

Author:

Kakeu Ariane G. Tallee¹,Strüngmann Lutz²,Njionou Blaise B. Koguep¹,Lele Celestin¹

Affiliation:

1. Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, West Region, Cameroon

2. Faculty of Computer Science, Mannheim University of Applied Sciences, Mannheim 68163, Germany

Abstract

This study aims to introduce the concept of [Formula: see text]-ideal in bounded commutative residuated lattices and establish some related properties. In this paper, we show that the set of [Formula: see text]-ideals of a bounded commutative residuated lattice is a Heyting algebra, and an algebraic lattice. Moreover, we state the prime [Formula: see text]-ideal theorem, and describe relations between [Formula: see text]-ideals and some types of ideals of a bounded commutative residuated lattice. Finally, we discuss correspondences between [Formula: see text]-ideals and [Formula: see text]-filters of a bounded commutative residuated lattice.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Computer Science Applications,Human-Computer Interaction

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793005723500254

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