Coproduct in the category of algebras

Ulmo

Hi

I've tried searching the web for information on how to construct the coproduct in the category of (noncommutative) algebras over a ring. I know that in the commutative case it is the tensor product, but I've been told that there exists a general construction as well, akin to the free product of groups (at least in some cases).

Can anyone help me with this?