Radical and Jacobson Radical in L-Algebras

Rajab Ali Borzooei; Hamideh  Khajeh Nasir; Mehdi Yavari

doi:10.18778/0138-0680.2026.14

Authors

Rajab Ali Borzooei Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran; Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkiye Author https://orcid.org/0000-0001-7538-7885
Hamideh Khajeh Nasir Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran Author
Mehdi Yavari Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran Author

DOI:

https://doi.org/10.18778/0138-0680.2026.14

Keywords:

L-algebra, CKL-algebra, ideal, radical of an ideal, Jacobson radical

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.

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