α-Ideals in Bounded Commutative Residuated Lattices
Ariane G. Tallee Kakeu, Lutz Strüngmann, Blaise B. Koguep Njionou, Célestin Lélé · New Mathematics and Natural Computation · 2022
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.