Derivasi di Pseudo BG-aljabar

Ayuni Putri; Sri Gemawati; Syamsudhuha Syamsudhuha

doi:10.37905/jjom.v7i1.28306

Derivasi di Pseudo BG-aljabar

Ayuni Putri, Sri Gemawati, Syamsudhuha Syamsudhuha

Abstract

A BG-algebra is defined as a non-empty set that includes a constant 0 and a binary operation which adheres to the following axioms: (𝐵G1) , (𝐵G2) , and (𝐵G3) for all . Pseudo BG-algebra is a generalization of BG-algebra, which is an algebra that satisfies the following axioms: (pBG1) , (pBG2) , and (pBG3) for all . In BG-algebra introduced an (l, r)-derivation, an (r, l)-derivation, and left derivation. This article aims to discuss and develop the concept of derivations in pseudo BG-algebras by introducing two new operations, and , within the structure of pseudo BG-algebra . These operations are defined as and for each . In this research, the operation in BG-algebra derivations replaced with the and operations under certain conditions, leading to the formulation of new types of derivations. Through this approach, three main types of derivations in pseudo BG-algebras are identified: (l, r)-derivation, (r, l)-derivation, and left derivation of type 1 and type 2. The results reveal several significant properties, including a formula for , the role of the special element 0, regularity in derivations, and the relationship between regular derivations and as the identity function. This study contributes to advancing the theory of pseudo BG-algebras and its potential applications in other algebraic structures.

Keywords

Pseudo BG-algebra; (l, r)-derivation; (r, l)-derivation; left derivation; type 1 derivation; type 2 derivation

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DOI: https://doi.org/10.37905/jjom.v7i1.28306