Upper Sets on Generalized $\Gamma$-BE-algebras
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i2.6546Keywords:
BE-algebra, $\Gamma$-BE-algebra, $\Gamma_{(\alpha, \beta)}$-BE-algebra, $\Gamma_{\Delta}$-BE-algebra, subalgebra, filterAbstract
We introduce $\Gamma_\Delta$-BE-algebras as a generalization of Γα- and Γ(α,β)-BE-algebras, and specify the algebraic conditions that govern this new structure. We investigate their fundamental properties, define the notions of ∆-subalgebras and ∆-filters, and examine their interrelations. Furthermore, we explore the behavior of two types of upper sets, $E_\alpha(x)$ and $E^\beta_\alpha(x, y)$, within the framework of ∆-left distributive Γ∆-BE-algebras, providing several characterizations and structural results. These findings offer a broadened perspective on algebraic systems related to BE-algebras and their logical extensions.
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Copyright (c) 2026 Wongsakron Sukhon, Attaphol Pumila, Pongpun Julatha, Aiyared Iampan
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