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New Proofs for two Theorems of Capelli
Published online by Cambridge University Press: 20 November 2018
Extract
The following two theorems are due to Capelli.
THEOREM 1. Let g(x) and h(x) be polynomials over a field R of characteristic 0; let f(x) = g(h(x)). Then f(x) is irreducible over R if and only if
(i) g(x) is irreducible over R
and
(ii) h(x) - β is irreducible over R(β), where β is a root of g(x).
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- Copyright © Canadian Mathematical Society 1964
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