📚 noun • entry_id 60674
splitting field
Meanings (ES + gloss)
cuerpo de descomposición
(of a polynomial) Given a polynomial p over a field K, the smallest extension field L of K such that p, as a polynomial over L, decomposes into linear factors (polynomials of degree 1); (of a set of polynomials) given a set P of polynomials over K, the smallest extension field of K over which every polynomial in P decomposes into linear factors.
In the case of the polynomial t²#43;1#92;in#92;R#91;t#93;, the situation is quite clear; its splitting field is #92;C since t²#43;1#61;(t#43;i)(t-i) where i#61;#92;sqrt#123;-1#125;…
Theorem 3.2. If K is a field and f#92;inK#91;x#93; has degree n#92;ge 1, then there exists a splitting field F of f with #91;F#58;K#93;#92;len#33;
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