Multiplier in BL-algebras

Abstract

In this paper, we introduce the notion of multiplier in -algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and ( -derivations in -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 and study some properties. Finally, we show that if is a boolean algebra, then the set of all multipliers of is a -algebra under some conditions.