Some properties of a new class on monadic BL-algebras

In this article, we develop the significance of monadic BL-algebras via adding a clause that describes properties of a perfect monadic BL-algebra. Then, some Theorems that prove some of their elementary properties are given. The relationship between perfect monadic filters and the quotient algebras have been considered. It is shown a monadic BL-algebra is perfect if and only if every monadic filter of its is perfect.