Neighborhood systems and irreducible filters in L-algebras

Ebrahimi, Mohamad; Park, Choonkil

doi:10.22103/jmmr.2026.26754.1934

Neighborhood systems and irreducible filters in L-algebras

Articles in Press

Document Type : Research Paper

Authors

Mohamad Ebrahimi ¹

Choonkil Park ²

¹ Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

² Research Institute for Convergence of Basic Science, Hanyang University, Seoul, Korea

10.22103/jmmr.2026.26754.1934

Abstract

In this respect, the concept of an $L$-algebra $L$ is revisited and after that, the article is prepared to deal with the notion of irreducible filters of $L$. Some basic properties of irreducible filters are investigated. In the following, the concept of a neighborhood of a point in an $L$-algebra is defined, and its connection with the notion of a filter is investigated. The article establishes conditions under which a filter can be expressed as a union of these neighborhoods and in special cases, every filter is itself a neighborhood. These neighborhoods can also form the foundation of a topological structure on $L$-algebras that a person can pursue in the future.

Keywords

The new key words: L-algebra

irreducible filter

neighborhood

congruence

Subjects

Fuzzy Mathematics and Soft Computing

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