compositumとは 意味・読み方・使い方

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 ${\displaystyle \mathbb {Q} }$, we get the maximal abelian extension by adjoining all roots of unity, i.e., taking compositum of all ${\displaystyle m}$-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 ${\displaystyle F({\sqrt {a_{i}}})}$ in the algebraic closure of ${\displaystyle F}$.

使用する際の注意点

• Denoted ${\displaystyle A\cdot B}$.
• It is the same as the image of the homomorphism ${\displaystyle h:(A\otimes _{k}B)\to F}$ that maps the tensor product ${\displaystyle a\otimes b\to ab}$.

同意語

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

Further reading

• Tensor product of fields#Compositum of fields on Wikipedia.
• Compositum on Encyclopedia of Mathematics

Latin

語源

Inflected form of compositus; the noun is the substantivised neuter form.

形容詞

compositum

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

名詞

compositum n (genitive compositī); second declension

1. that which is agreed; an agreement, compact, etc.

   Synonyms: condiciō, stipulātiō, pactum

2. compound word, compound

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.

語形変化

Second-declension noun (neuter).

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