It seems that ETS has never given any standard references for the terminologies that are used in the GRE Sub Mathematics exam. While in the Cracking the GRE Mathematics Subject Test, a ring has been defined as not requiring the existence of a multiplicative identity, i.e. the unity, which affects a number of related concepts too, the subring, the ring homomorphism etc. However, in most algebra books (for instance, Jacobson's), such an object is given the name rng, and the ring is always assumed to have a unity. So what's the ETS's definition of a ring?