Reference request: extending tensor product of modules

Question

I'm looking for a reference to a construction similar to the following.

I have a right R-module, $A_{K'}$, and a left R-module, $_KB$, where $K$ and $K'$ are fields and $K'\subset K$. I want to take the tensor product of the two modules over $K'$, so I have $A \otimes_{K'}B$ with elements satisfying

1. $(a_1 + a_2)\otimes b=a_1\otimes b+a_2\otimes b$
2. $a\otimes (b_1 +b_2)=a\otimes b_1 +a\otimes b_2$
3. $(ak')\otimes b= a\otimes(k'b)$

where $a, a_1, a_2 \in A$, $b,b_1,b_2\in B$ and $k'\in K'$. Then extend 3. to allow scalar multiplication by all elements of $K$ with $k(a\otimes b)= a\otimes kb$.

I've been told this is a standard construction but I can't find anywhere it has been used.

Thank you :)