compositum
English
editEtymology
editFrom Latin compositum.
Noun
editcompositum (plural compositums)
- (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 , we get the maximal abelian extension by adjoining all roots of unity, i.e., taking compositum of all -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 in the algebraic closure of .
- 1998, Iain T. Adamson (translator), David Hilbert, The Theory of Algebraic Number Fields, [1897, D. Hilbert, Zahlbericht], Springer, page 98,
Usage notes
edit- Denoted .
- It is the same as the image of the homomorphism that maps the tensor product .
Synonyms
edit- (smallest subextension of a given field extension that contains two given subextensions): field compositum
Translations
editsmallest subextension of a given field extension that contains two given subextensions
Further reading
edit- Tensor product of fields on Wikipedia.Wikipedia
- Compositum on Encyclopedia of Mathematics
Latin
editEtymology
editInflected form of compositus; the noun is the substantivised neuter form.
Adjective
editcompositum
- inflection of compositus:
Noun
editcompositum n (genitive compositī); second declension
- that which is agreed; an agreement, compact, etc.
- Synonyms: condiciō, stipulātiō, pactum
- compound word, compound
Usage notes
edit- 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.
Declension
editSecond-declension noun (neuter).
Case | Singular | Plural |
---|---|---|
Nominative | compositum | composita |
Genitive | compositī | compositōrum |
Dative | compositō | compositīs |
Accusative | compositum | composita |
Ablative | compositō | compositīs |
Vocative | compositum | composita |
References
edit- “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
- (ambiguous) well-ordered, well-brushed hair: capilli compti, compositi (opp. horridi)
Categories:
- English terms derived from Latin
- English lemmas
- English nouns
- English countable nouns
- en:Algebra
- English terms with quotations
- Latin non-lemma forms
- Latin adjective forms
- Latin lemmas
- Latin nouns
- Latin second declension nouns
- Latin neuter nouns in the second declension
- Latin neuter nouns
- Latin words in Meissner and Auden's phrasebook