In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters. (2000): 06F35, 03G25. Mathematics Subject Classification

Key words n-fold (positive) implicative basic logic, n-fold (positive) implicative BL-algebra, n-fold (positive) implicative filter, Gödel algebra, Boolean algebra. MSC (2000) 06F35, 03G25In this paper we introduce n-fold (positive) implicative basis logic and the related algebras called n-fold (positive) implicative BL-algebras. Also we define n-fold (positive) implicative filters and we prove some relations between these filters and construct quotient algebras via these filters.

In this paper, we consider a collection of filters of a BL-algebra A. We use the concept of congruence relation with respect to filters to construct a uniformity which induces a topology on A. We study the properties of this topology regarding different filters.

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