splitting fields

A form of splitting field — (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.

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Meanings

noun
  1. pluralplural of splitting field
Cite this entry
APA

splitting fields. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/splitting%20fields

MLA

“splitting fields.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/splitting%20fields. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “splitting fields,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/splitting%20fields.

Source: splitting fields on Wiktionary, CC BY-SA 4.0.