Linearly disjoint

In mathematics, algebras A, B over a field k inside some field extension ${\displaystyle \Omega }$ of k are said to be linearly disjoint over k if the following equivalent conditions are met:

Note that, since every subalgebra of ${\displaystyle \Omega }$ is a domain, (i) implies ${\displaystyle A\otimes _{k}B}$ is a domain (in particular reduced). Conversely if A and B are fields and either A or B is an algebraic extension of k and ${\displaystyle A\otimes _{k}B}$ is a domain then it is a field and A and B are linearly disjoint. However there are examples where ${\displaystyle A\otimes _{k}B}$ is a domain but A and B are not linearly disjoint: for example, A=B=k(t), the field of rational functions over k.

...
Wikipedia