A rng is an associative ring without necessarily having a multiplicative identity (rng = ring - $i$dentity).

The term *rng* (pronounced "rung") is used to refer to an associative ring which does not necessarily have an identity element. (rng = ring - **i**dentity). Use this tag if your question particularly is about certain conditions forcing the existence of identity, or a morphism preserving identity. Using this tag along with ring-theory or abstract-algebra will be appreciated.