Multiplier in BL-algebras

In this paper, we introduce the notion of multiplier in BL-algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and (circle dot,V)-derivations in BL-algebras. We introduce the concept of idempotent multipliers in BL-algebra and weak congruence and obtain an interconnection between idempotent multipliers and weak congruences. Also, we introduce the special multiplier alpha(p) and study some properties. Finally, we show that if A is a boolean algebra, then the set of all multipliers of A is a BL-algebra under some conditions.