α-Ideals in Bounded Commutative Residuated Lattices

Ariane G. Tallee Kakeu, Lutz Strüngmann (), Blaise B. Koguep Njionou () and Celestin Lele ()
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Ariane G. Tallee Kakeu: Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, West Region, Cameroon
Lutz Strüngmann: Faculty of Computer Science, Mannheim University of Applied Sciences, Mannheim 68163, Germany
Blaise B. Koguep Njionou: Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, West Region, Cameroon
Celestin Lele: Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, West Region, Cameroon

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 03, 611-630

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

Keywords: Bounded commutative residuated lattice; Heyting algebra; ideal; prime ideal; annihilator; α-ideal (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005723500254

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