This research introduces a framework for generating strong d-algebras through polynomial operations, suggesting new criteria for their classification.
In this paper, we investigate the interplay between polynomials and algebraic structures on the real numbers, with a focus on characterizing and constructing strong d-algebras. We introduce a systematic framework for generating such algebras through constructive function triples of functions $(f,g,h)$ defined by polynomial operations that satisfy axioms generalizing classical derivations. By leveraging polynomial definitions, we establish new sufficient and necessary conditions for a d-algebra on to qualify as ``{ strong}", thereby expanding the known criteria in the literature.
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Ghadimi et al. (2025) studied this question.
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