Novel Homomorphic Characteristics of PU-Algebra in Relation to Discrete Dynamical Systems (Global Journal of Sciences, 2025)
PU-algebra theory plays a pivotal role in various applied domains, including information sciences, cybernetics, computer science, and artificial intelligence. This work advances the theoretical understanding of PU-algebras, with a particular emphasis on their homomorphic properties. We explore foundational properties of PU-algebras, focusing on characterizing ideals and subalgebras by introducing discrete dynamical system concepts for instance periodic points, fixed points, invariant sets, and strongly invariant sets within the PU-algebraic framework. Here, (, ) denotes a discrete dynamical system where is a PU-algebra and a homomorphism on . The findings not only deepen the theoretical foundation of PU-algebras but also pave the way for future applications in modeling complex dynamical systems and automata theory. This research opens several avenues for further study, including the development of algorithms for computational representation of PU-algebraic structures and the exploration of their utility in enhancing machine learning models and artificial intelligence systems. Additionally, gaps in understanding the interaction between PU-algebra properties and advanced dynamical system concepts suggest a promising direction for future investigation.
Keywords: PU-Algebra; Periodic points; Fixed points; Invariant set