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An element $x$ of ring $R$ is called idempotent if $x^2 = x$.
Which rings do not have idempotent elements other than $0$ and $1$?
Nontrivial commutative ring $R$
Nontrivial cancellative ring $R$
Ring $R$ with no nontrivial nilpotent elements
Ring $R$ with $y \ne 0, 1$, and $y^2 = y^4$