# 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