At < https://mathoverflow.net/questions/219864/when-does-r-x-i-have-infinitely-many-idempotents >, Er_Ro asked the following question. 

> Let $R $ be a commutative ring with identity and $R[x] $ its polynomial ring. I am looking for a ring with finitely many idempotent and an unextended ideal $I $ in $R [x] $ such that $R[x]/I$ has infinitely many idempotent? 


It is important and whenever $R $ is a semilocal non Notherian ring, I want to know that is there any example in this case.