separable

See also: séparable

English

Etymology

From Middle English separable, from Middle French separable and its etymon Latin sēparābilis.[1][2]

Pronunciation

  • Audio (Southern England):(file)

Adjective

separable (comparative more separable, superlative most separable)

  1. Able to be separated.
  2. (mathematics, 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. (mathematical analysis, of a topological space) Having a countable dense subset.
  4. (mathematics, algebra) Any of several technical senses relating to the behavior of polynomials or objects over which polynomials can be defined:
    1. (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)
      x2+1 is separable, since its roots are i and −i.
      1. (Galois theory, obsolete, of a polynomial P) Such that none of the irreducible factors of P have a repeated root.
    2. (Galois theory, of an algebraic field extension E/F) Such that the minimal polynomial of every element of E is a separable polynomial.
    3. (abstract algebra, of an algebra over a ring) 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

Synonyms

Antonyms

Derived terms

Translations

References

  1. ^ “sē̆parāble, adj.”, in MED Online, Ann Arbor, Mich.: University of Michigan, 2007.
  2. ^ “separable, n.”, in OED Online Paid subscription required⁠, Oxford: Oxford University Press, launched 2000.

Anagrams

Asturian

Adjective

separable (epicene, plural separables)

  1. separable

Catalan

Etymology

    Learned borrowing from Latin sēparābilis.

    Pronunciation

    Adjective

    separable m or f (masculine and feminine plural separables)

    1. separable
      Antonym: inseparable

    Further reading

    Spanish

    Etymology

    Etymology tree
    Proto-Indo-European *s(w)é
    Proto-Indo-European *s(w)ēdder.
    Latin sē-
    Proto-Indo-European *perh₃-
    Proto-Indo-European *pr̥h₃o-
    Proto-Italic *paro-
    Proto-Indo-European *-h₂
    Proto-Indo-European *-éh₂
    Proto-Indo-European *-yéti
    Proto-Indo-European *-eh₂yéti
    Proto-Indo-European *-h₂tiinflu.
    Proto-Italic *-ājō
    Proto-Italic *-āō
    Latin -ō
    Latin parō
    Latin sēparō
    Proto-Indo-European *-dʰlom
    Proto-Italic *-ðlom
    Proto-Italic *-ðlis
    Latin -bilis
    Latin sēparābilisder.
    Spanish separable

      Derived from Latin sēparābilis.

      Pronunciation

      • IPA(key): /sepaˈɾable/ [se.paˈɾa.β̞le]
      • Rhymes: -able
      • Syllabification: se‧pa‧ra‧ble

      Adjective

      separable m or f (masculine and feminine plural separables)

      1. separable, detachable
        Antonym: inseparable

      Further reading

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