Exponential Fields: Lack of Generic Derivations
Fornasiero Antongiulio, Giuseppina Terzo
TL;DR
This paper explores the limitations of exponential fields in supporting generic derivations, demonstrating that without specific compatibility conditions, such derivations cannot exist.
Contribution
It proves that exponential fields lacking certain compatibility conditions cannot admit generic derivations, clarifying the structural constraints.
Findings
Exponential fields without compatibility conditions lack generic derivations.
The paper establishes necessary conditions for the existence of generic derivations.
It advances understanding of the algebraic structure of exponential fields.
Abstract
We investigate the existence of "generic derivations" in exponential fields. We show that exponential fields without additional compatibility conditions between derivation and exponentiation cannot support a generic derivation.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems