On Kronecker's Solvability Theorem
Yan Pan, Yuzhen Chen

TL;DR
This paper revisits Kronecker's 1856 solvability theorem, providing a natural derivation using a polynomial complete decomposition method and addressing gaps in previous proofs.
Contribution
It introduces a new derivation of Kronecker's solvability theorem through a polynomial decomposition method, improving upon D"orrie's approach.
Findings
Provides a complete and gap-free proof of Kronecker's solvability theorem
Demonstrates the method's effectiveness in constructing unsolvable algebraic equations
Enhances understanding of polynomial decomposition techniques
Abstract
Kronecker's 1856 paper contains a solvability theorem that is useful to construct unsolvable algebraic equations. We show how Kronecker's solvability theorem can be derived naturally via a polynomial complete decomposition method. This method is similar to D\"orrie, but we fill a gap that appears in his proof.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Polynomial and algebraic computation
