When "I" is finite, the underlying additive group of coincides with the direct sum of the additive groups of the "R""i". In this case, some authors call "R" the "direct sum of the rings "R""i"" and write , but this is incorrect from the point of view of category theory, since it is usually not a coproduct in the category of rings: for example, when two or more of the "R""i" are nonzero, the inclusion map fails to map 1 to 1 and hence is not a ring homomorphism.