α-Ideals in Bounded Commutative Residuated Lattices.

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. [ABSTRACT FROM AUTHOR]