The direct product of the rings 
, for 
some index set 
, is the set
 |
The ring direct product is confusingly also called the complete direct sum (Herstein 1968).
The ring direct product, like the group direct product, has the universal property that
if any ring 
has a homomorphism to 
and a homomorphism to 
, then these homomorphisms factor through 
in a unique way.
