Let $R $ be a commutative ring with identity and $R[x] $ its polynomial ring. If $I$ is an ideal of $R[x] $, we know that $R[x] /I$ has no nontrivial idempotent if and only if $R[x]/ I$ is an indecomposiable ring. I want to know that is there any equivalent conditions (Specially, on the generators of $I $) for $I$ with the above properties?