Phrase guide

separable polynomial

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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Pronunciation

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1

noun

Meaning 1

A polynomial over a given field that has distinct roots in the algebraic closure of said field (the number of roots being equal to the degree of the polynomial).

Definition source: English Wiktionary via Wiktextract

Qualifier: field theory

Topics: algebra, mathematics, sciences

Examples

  • Over a perfect field, the separable polynomials are precisely the square-free polynomials.
  • The study of the automorphisms of splitting fields of separable polynomials over a field is referred to as Galois theory.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

3 source translations are retained for this English entry.

  • Italian: polinomio separabile — polynomial that has distinct roots
  • Polish: wielomian rozdzielny — polynomial that has distinct roots
  • Spanish: polinomio separable — polynomial that has distinct roots