n-Fold Fantastic and n-Fold Involutive Ideals in Bounded Commutative Residuated Lattices

Abstract

In this paper, we introduce the concepts of n-fold obstinate ideals, n-fold normal ideals, n-fold fantastic ideals and n-fold involutive ideals in residuated lattices, state and prove some of their properties. Several characterizations of these notions are derived and the relations between those notions are investigated. Also, we construct the correspondence between the notions of n-fold ideal and n-fold filter in residuated lattices.

Keywords

• residuated lattice
• ideal
• n-fold ideal
• n-fold filter
• 06b10
• 06b99
• 03g10