SOME EXTENSIONS FROM BL-ALGEBRAS TO MTL-ALGEBRAS

In this work we show that we can extend some theorems and definitions from BL-algebras to MTL-algebras. We know that a BL-algebra L is called an MV algebra ifx^ = x for all x ∈ L or equivalently (x → y) → y = (y → x) → x for all x, y ∈ L. We prove that this definition is true for the MTL-algebras. Similarly we prove that an MTL-algebra L is called a Go ̈del algebra if x^2= x⨀x = x for all x ∈ L, therefore we can extend some theorems that satisfy in these definitions from BL-algebras to MTL-algebras.