Stabilizers on \(L\)-algebras

Gholam Reza Rezaei; Mona Aaly Kologani

doi:10.18778/0138-0680.2023.28

Authors

Gholam Reza Rezaei University of Sistan and Baluchestan, Department of Mathematics, Zahedan, Iran
Mona Aaly Kologani Hatef Higher Education, Zahedan, Iran https://orcid.org/0000-0002-5234-2876

DOI:

https://doi.org/10.18778/0138-0680.2023.28

Keywords:

\(L\)-algebra, stabilizer, ideal, co-anihiliators, Baire space, topological space

Abstract

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.

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