Radical and Jacobson Radical in L-Algebras

Abstract

In this paper, inspired by the concepts of the radical of an ideal and the Jacobson radical in ring theory, we introduce these notions in the context of L-algebras. Our main goal is to explore the nature of the radical of an ideal and Jacobson radical in specific L-algebras. We successfully identify the elements of these radicals in special classes of L-algebras, including proper Glivenko algebras and finite Brouwerian semi-lattices using a closure operator. To achieve this goal, we introduce a new notion that is associated with any element a ∈ L as well as with an ideal of an L-algebra L.