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math.AC2026
An elementary algebraic proof of the fundamental theorem of algebra
Katelyn S. Clark, Pace P. Nielsen
We provide a new, elementary, algebraic proof of the fundamental theorem of algebra. Furthermore, the method recovers a more general version of the theorem recently obtained by Jos…
math.AC2025
Euclidean domains with no multiplicative norms
Caleb J. Dastrup, Pace P. Nielsen
We construct a Euclidean domain with no multiplicative Euclidean norm to a compatibly well-ordered monoid, and hence with no multiplicative Euclidean norm to (under it…