On residuated <i>n</i> -lattice

Abstract In this paper, we introduce residuated n-lattice: a variety of residuated semigroup equipped with binary hyperoperations n-sup and n-inf. We define the left bound, right bound, n-supremum, n-infimum, maximum and minimum with respect to it′s relation. By these way, the notion of residuated semigroup has been generalized. Some examples of residuated n-lattice have been gave, then we show that our definition is an extention of the old ones. Also, we state and prove some theorems in this structure.