separable polynomial
separable polynomial noun: 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).
Noun
separable polynomial (plural separable polynomials)
- 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).
- 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.
separable polynomial meaning in Tamil
separable polynomial in Tamil
- பிரித்தகு பல்லுறுப்பான்
Examples of separable polynomial in a sentence
- We know that F(#92;zeta) is a normal extension because it is the splitting field of the separable polynomial xⁿ-1 (see Theorem 7.5).1978, Marvin Marcus, Introduction to Modern Algebra, M. Dekker, page 277:
- Proposition 1.4.2 A finite field extension M#47;K is Galois if and only if M is the splitting field over K of a separable polynomial.2005, Arne Ledet, Brauer Type Embedding Problems, American Mathematical Society, page 6:
Forms of separable polynomial
| plural | separable polynomials |
|---|
Words formed from separable polynomial
- discriminantly separable polynomial
Questions about separable polynomial
- What does separable polynomial mean?
- Separable polynomial means 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).
- What is separable polynomial in Tamil?
- Separable polynomial in Tamil is பிரித்தகு பல்லுறுப்பான். See Separable polynomial meaning in Tamil.
- How do you use separable polynomial in a sentence?
- We know that F(#92;zeta) is a normal extension because it is the splitting field of the separable polynomial xⁿ-1 (see Theorem 7.5).
- What part of speech is separable polynomial?
- Separable polynomial is a noun.
- What is the plural of separable polynomial?
- The plural of separable polynomial is separable polynomials.
Words near separable polynomial in the dictionary
Source and license
Adapted from Wiktionary: separable polynomial (page history and authors); separable polynomial (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Cite this entry: “separable polynomial.” Word.ws, https://word.ws/separable_polynomial. Based on Wiktionary, CC BY-SA 4.0.