A constructive version of Laplace's proof on the existence of complex roots
Abstract
Laplace presented an algebraic proof of the fundamental theorem of algebra which relied on the existence of a splitting field. This proof can be generalized by replacing real numbers by any real closed field. Although it is possible to build a splitting field in a classical context, it is not true anymore in an constructive context. We present a constructive version of Laplace's proof as the result of a general method to make constructive sense of the notion of splitting fields.
Domains
Rings and Algebras [math.RA]
Origin : Files produced by the author(s)
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