Double left stabilizers in BL-algebras

Abstract

In this paper we introduce the notions of double left stabilizer of X and double left stabilizer of X with respect to Y, for nonempty subsets X and Y of BL-algebra A and we study some properties of them. After that we state and prove some theorems which determine the relationship between these notions and other types of filters in BL-algebras. Finally we introduce the set N(F), for every filter F of A. Also we prove A is an MV-algebra iff N(F)=N(A)={\$ iff$D(X_l)=X_l iff $D((X,{1})_l)=X_l, for each nonempty subset X and every proper filter F of A.