Group Structures and Derivations on PMS-algebras

Background PMS-algebras are a specific algebraic structure that generalizes a propositional algebra called BCK-algebra. This paper delves into the intricate group structure of these algebras and the concept of derivations within this framework. Methods We employ rigorous mathematical techniques to analyze the properties of derivations in P MS-algebras. This involves examining various characteristics of derivations and investigating their behavior in specific subcategories, such as torsion-free P MS-algebras. Results Our research reveals several key findings. Firstly, we establish that the set of all derivations associated with the binary operation defined on a P MS-algebra constitutes a semigroup. Secondly, we provide a comprehensive analysis of generalized derivations, d-invariant ideals, fixed sets, and torsion-free P MS-algebras within the context of P MS-algebras. Conclusions This study contributes to a deeper understanding of the algebraic structure of P MS-algebras and the role of derivations within this context. The findings presented here have implications for further research in abstract algebra and related fields.