Perfect and Local Bounded Equality Algebras

Sogol Niazian; Mona Aaly Kologani; Young Bae Jun; Rajab Ali Borzooei

doi:10.18778/0138-0680.2026.18

Authors

Sogol Niazian Faculty of Medicine, TeMS. C, Islamic Azad University, Tehran, Iran Author https://orcid.org/0000-0002-1064-4139
Mona Aaly Kologani Hatef Higher Education Institute, Zahedan, Iran Author https://orcid.org/0000-0002-5234-2876
Young Bae Jun Department of Mathematics, Gyeongsang National University, Korea Author https://orcid.org/0000-0002-0181-8969
Rajab Ali Borzooei Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkiye; Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran Author https://orcid.org/0000-0001-7538-7885

DOI:

https://doi.org/10.18778/0138-0680.2026.18

Keywords:

bounded equality algebra, local (perfect, integral) bounded equality algebras, primary filter, perfect filter

Abstract

In this paper, by considering the notion of bounded equality algebra, we introduce the concepts of perfect, integral and local bounded equality algebras and we state and prove some related results. Specially, we define the notions of some filters such as primary and perfect filters and we get the relation between perfect filters with perfect bounded equality algebras and primary filters in the local bounded equality algebras. Finally, by defining the concepts of radical, locally finite, and peculiar bounded equality algebra, we give a representation for any bounded p-equality and local bounded equality algebras.

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