Q:

Ring Theory: Identity Elements

A brief question$:$ If a ring is specified to have an identity, is it implicit that the identity in question is the multiplicative identity? From the definition of a ring $R$, $R$ must contain additive identity to begin with.
Thanks in advance, I couldn't figure this out from rereading my text.

A:

Yes. If a ring $(R, +, \cdot)$ is said to have an identity, that means specifically the identity of $(R, \cdot)$. 
As you pointed out earlier, all rings have an additive identity since $(R, +)$ must be a group.

