compositum

== English == === Etymology === From Latin compositum. === Pronunciation === === Noun === compositum (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. ==== Usage notes ==== Denoted A ⋅ B {\displaystyle A\cdot B} . It is the same as the image of the homomorphism h : ( A ⊗ k B ) → F {\displaystyle h:(A\otimes _{k}B)\to F} that maps the tensor product a ⊗ b → a b {\displaystyle a\otimes b\to ab} . ==== Synonyms ==== (smallest subextension of a given field extension that contains two given subextensions): field compositum ==== Translations ==== === Further reading === Tensor product of fields on Wikipedia.Wikipedia Compositum on Encyclopedia of Mathematics == Latin == === Etymology === Inflected form of compositus; the noun is the substantivised neuter form. === Adjective === compositum inflection of compositus: nominative/accusative/vocative neuter singular accusative masculine singular === Noun === compositum n (genitive compositī); second declension that which is agreed; an agreement, compact, etc. Synonyms: condiciō, stipulātiō, pactum compound word, compound ==== Usage notes ==== 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 ==== Second-declension noun (neuter). === References === “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.