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Difference between revisions of "Compositum"

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''of field extensions''
 
''of field extensions''
  
The smallest subextension <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024310/c0243101.png" /> of an extension <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024310/c0243102.png" /> of a field <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024310/c0243103.png" /> containing two given subextensions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024310/c0243104.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024310/c0243105.png" />. It is the same as the image of the homomorphism <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024310/c0243106.png" /> that maps the tensor product <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024310/c0243107.png" /> to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024310/c0243108.png" />.
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The smallest subextension $A \mathbin{.} B$ of an extension $\Omega$ of a field $k$ containing two given subextensions $A \subset \Omega$ and $B \subset \Omega$. It is the same as the image of the homomorphism $ \phi : A \otimes_{k} B \to \Omega$ that maps the tensor product $a \otimes b$ to $ab \in \Omega$.

Latest revision as of 21:46, 22 October 2017

of field extensions

The smallest subextension $A \mathbin{.} B$ of an extension $\Omega$ of a field $k$ containing two given subextensions $A \subset \Omega$ and $B \subset \Omega$. It is the same as the image of the homomorphism $ \phi : A \otimes_{k} B \to \Omega$ that maps the tensor product $a \otimes b$ to $ab \in \Omega$.

How to Cite This Entry:
Compositum. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compositum&oldid=11305