TL;DR
This paper shows that derivations in ring theory can be characterized by a single equation, simplifying the understanding of their properties beyond traditional additivity-based characterizations.
Contribution
It introduces a novel single-equation characterization of derivations, moving beyond the conventional additivity plus property framework.
Findings
Derivations can be characterized by a single algebraic equation.
This new characterization simplifies the understanding of derivations.
The approach broadens the theoretical framework for ring derivations.
Abstract
Although the characterization of ring derivations has an extensive literature, up to now, all of the characterizations have had the following form: additivity and another property imply that the function in question is a derivation. The aim of this note is to point out that derivations can be described via a single equation.
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