Pre-Hilbert Algebras with Condition (GE3)

Akbar Rezaei; Arsham Borumand Saeid

doi:10.18778/0138-0680.2026.26

Authors

Akbar Rezaei Payame Noor University, Department of Mathematics, Tehran, Iran Author https://orcid.org/0000-0002-6003-3993
Arsham Borumand Saeid Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer, Kerman, Iran Author https://orcid.org/0000-0001-9495-6027

DOI:

https://doi.org/10.18778/0138-0680.2026.26

Keywords:

RML algebra, pi-RML algebra, pre-BBBCC algebra, pi-pre-BBBCC algebra, BCK-algebra, (self distributive) BE-algebra, (transitive) GE-algebra

Abstract

GE-algebras are introduced as a generalization of Hilbert algebras in 2020. In this paper, we show that a self distributive GE-algebra is equivalent to the pimpl-RML algebra, and a transitive GE algebra is equivalent to the pi-pre-BBBCC algebra with condition (An). Further, we prove that pimpl-BE algebras are a subclass of pimpl-RML algebras and pre-Hilbert algebras with condition (GE3) are equivalent to the pi-pre-BBBCC algebras with condition (An).

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