Derivasi di Pseudo BG-aljabar - Putri, Ayuni; Gemawati, Sri; Syamsudhuha, Syamsudhuha (Jambura Journal of Mathematics, 2025)
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: (ðµG1) , (ðµG2) , and (ðµG3)  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.