Difference between revisions of "Compositum"
From Encyclopedia of Mathematics
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| − | The smallest subextension | + | 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=42170
Compositum. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compositum&oldid=42170