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compositum

名詞

compositum (複数形 compositums)

1. (algebra, field theory) Given a field extension F/K and subextensions A and B, the smallest subextension that contains both A and B.
   • 1998, Iain T. Adamson (translator), David Hilbert, The Theory of Algebraic Number Fields, [1897, D. Hilbert, _Zahlbericht_], Springer, page 98,
     Of particular interest is the case in which the discriminants of the fields forming the compositum are relatively prime.
   • 2004, Dinesh S. Thakur, Function Field Arithmetic, World Scientific, page 81,
     For Q {\displaystyle \mathbb {Q} } , we get the maximal abelian extension by adjoining all roots of unity, i.e., taking compositum of all m {\displaystyle m} -th cyclotomic fields (this is the famous Kronecker-Weber theorem).
   • 2005, T. Y. Lam, Introduction to Quadratic Forms over Fields, American Mathematical Society, page 333,
     This is then just the field compositum of all the quadratic extensions F ( a i ) {\displaystyle F({\sqrt {a_{i}}})} in the algebraic closure of F {\displaystyle F} .

使用する際の注意点

同意語

• (smallest subextension of a given field extension that contains two given subextensions): field compositum

形容詞

compositum

1. inflection of compositus:
   1. nominative/accusative/vocative neuter singular
   2. accusative masculine singular

使用する際の注意点

• This noun also appears (in the ablative only) in the phrases ēx compositō (“according to agreement”, “by agreement”, “in concert”) and dē compositō (“by agreement”), as well as more rarely (in the same sense) alone as compositō.

参照

• “compositum”, in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
• compositum in Gaffiot, Félix (1934) Dictionnaire illustré latin-français, Hachette
• Carl Meißner; Henry William Auden (1894) Latin Phrase-Book‎[1], London: Macmillan and Co.
  • (ambiguous) well-ordered, well-brushed hair: capilli compti, compositi (opp. horridi)
  • (ambiguous) an elaborate speech: oratio composita
  • (ambiguous) well-arranged words: verba composita

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