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Published on: February 15, 2016
Group Structures and Derivations on PMS-algebras
Nibret Melese Kassahun1,2, Berhanu Assaye Alaba1, Yohannes Gedamu Wondifraw1
1Mathematics, Bahir Dar University, Bahir Dar, Amhara, 6000, Ethiopia.
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.
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