In this paper, we introduce the concepts of [Formula: see text]-fold boolean ideals, [Formula: see text]-fold implicative ideals and [Formula: see text]-fold integral ideals in residuated lattices and we state and prove 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 [Formula: see text]-fold ideal and [Formula: see text]-fold filter in residuated lattices.

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.