Compositum

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 $ab \in \Omega$.