Dictionary

separable en · ADJ

Pronunciation

• (Southern-England) audio

Etymology

From Middle English separable, from Middle French separable and its etymon Latin sēparābilis.

Meanings

1. Able to be separated.
2. (of a differential equation) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.
3. (of a topological space) Having a countable dense subset.
4. (of a polynomial) Any of several technical senses relating to the behavior of polynomials or objects over which polynomials can be defined: ▸ Having no repeated roots (where roots are considered in an algebraic closure)
   • x²#43;1 is separable, since its roots are i and -i.
5. (obsolete, of a polynomial, of a polynomial P, qualifier:Galois theory) Any of several technical senses relating to the behavior of polynomials or objects over which polynomials can be defined: ▸ Having no repeated roots (where roots are considered in an algebraic closure) ▸ Such that none of the irreducible factors of P have a repeated root.
6. (of an algebraic field extension E/F, qualifier:Galois theory) Any of several technical senses relating to the behavior of polynomials or objects over which polynomials can be defined: ▸ Such that the minimal polynomial of every element of E is a separable polynomial.
7. (abstract, of an algebra over a ring) Any of several technical senses relating to the behavior of polynomials or objects over which polynomials can be defined: ▸ Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia

Forms

Antonyms

combinable (antonym(s) of “able to be separated”) · annexable (antonym(s) of “able to be separated”) · inseparable (antonym(s) of “able to be separated”)

Deriveds

separable polynomial · separable prefix · nonseparable · unseparable · separable affix · semiseparable · quasiseparable · separable extension · superseparable · separableness · separably · separable verb

Relateds

separability

Synonyms

separatable · disunitable

Translations (32)

nl scheidbaar (able to be separated) · gl separable (able to be separated) · ja 可分の (able to be separated) · hu szétválasztható (able to be separated) · pl rozłączny ((differential equations)) · de separierbar ((differential equations)) · ca separable (able to be separated) · bg отделим (able to be separated) · ja 切り離せる (able to be separated) · pt separável ((differential equations)) · ast xebrable ((differential equations)) · sv delbar (able to be separated) · pt separável (able to be separated) · ca separable ((differential equations)) · de trennbar ((differential equations)) · de separabel (able to be separated) · it separabile (able to be separated) · fi separoituva (able to be separated) · es separable (able to be separated) · ru отделимый (able to be separated) · sv avtagbar (able to be separated) · fi erottuva (able to be separated) · es separable ((differential equations)) · hu elválasztható (able to be separated) · fr séparable ((differential equations)) · la sēparābilis (able to be separated) · gl separable ((differential equations)) · de trennbar (able to be separated) · sv separabel (able to be separated) · it separabile ((differential equations)) · ja 分離できる (able to be separated) · fi separoituva ((differential equations))