Recently, I have changed my vocabulary in abstract algebra.
If one doesn't require "ring" to have a unity, then one can say that "ring with unity $1\neq 0$"
However, I changed my vocabulary to call "a ring without unity" a rng, and "ring with unity" a ring.
With this vocabulary, how do I call "rings with unity $1\neq 0$"? Non-trivial ring I guess?
I want to know whether there is a common terminology to call that:)