on (semi)topology l-algebras

Here, we define (semi)topological l-algebras and some related results are approved. then we deduce conditions that mention an l-algebra to be a semi-topological or a topological l-algebra and we check some attributes of them. chiefly, we display in an l-algebra l, if (l, ↠, τ ) is a semi-topological l-algebra and {1} is an open set or l is bounded and satisfies the double negation property, then (l,τ) is a topological l-algebra. finally, we construct a discrete topology on a quotient l-algebra, under suit- able conditions. also, different kinds of topology such as t0 and hausdorff are investigated.