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At < When does $R [x]/I $ has 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.

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  • $\begingroup$ I guess this is the best way for you to do this as you cannot comment on the Er_Ro question or answer. $\endgroup$
    – Chris Ramsey
    Commented Oct 4, 2015 at 9:53

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