STABILIZERS ON L-ALGEBRAS.

The main goal of this paper is to introduce the notion of stabilizers in L-algebras and develop stabilizer theory in L-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a CKL-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in CKL-algebra are ideals. Then by using the right stabilizers we produced a basis for a topology on L-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology. [ABSTRACT FROM AUTHOR]