Tensor product of fields
= Tensor product of fields
{wiki}
The <tensor product of fields> $L\otimes_K M$ is a $K$-algebra, not necessarily a field. If $L$ and $M$ sit in one overfield, the map $l\otimes m\mapsto lm$ has an image that generates their compositum as a field. When the extensions are algebraic, this image is already a field. Injectivity of this multiplication map is equivalent to <linear disjointness>.