A debate in comments was raised by the question
the relevant part of which is
Let $R$ be a ring with $1$ and suppose $R$ has no zero divisors. Show that the only idempotents in $R$ are $0$ and $1$.
One of the answers went straight by assuming the ring $R$ is commutative, which, in my opinion, is too strong an assumption about the question at hand.
The aim of this metaquestion is thus establishing a general policy. It's true that conventions about naming rings are various and contradictory around the world, and I find the answer perfectly acceptable (albeit using a sledgehammer, in the particular case), provided “If the ring is commutative…” is added at the beginning.
To me, for example, rings are not commutative unless stated and I can't get from the question any hint about the OP considering this hypothesis.