separable polynomial
Word Rarity
Very rare
Frequency: Zipf frequency 2.41 in modern English
30
Scrabble Score
19
Letters
7
Syllables
12
Unique Chars
Meaning
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).
Example Sentences
- "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."
- "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)."
- "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."
- "If #92;pi#95;P is a separable polynomial in K#91;t#93;, then the derivative #92;partial#95;t#92;pi#95;P is prime to #92;pi#95;P in K#91;t#93;, and therefore a unit in K#91;t#93;#95;P.[…]In the case when #92;pi#95;P is an inseparable polynomial we may write #92;pi#95;P#61;f(t#123;pʳ#125;) for a suitable rgt;0 and separable polynomial f."