Characterizations of a Krull ring \(R[X]\) (Q2756099)

Let \(R\) be a commutative ring with identity. The author proves that \(R\) is a finite direct sum of Krull domains (respectively unique factorization domains) if and only if \(R[X]\) is a Krull (respectively factorial) ring, if and only if \(R\) is a normal Krull (respectively normal factorial) ring with a finite number of minimal prime ideals, if and only if \(R\) is a Krull (respectively factorial) ring with a finite number of minimal prime ideals and \(R_{M}\) is an integral domain for every maximal ideal \(M\) of \(R.\) It has been deduced that if \(R[X]\) is a Krull (respectively factorial) ring and if \(D\) is a Krull (respectively factorial) overring of \(R,\) then so is \(D[X].\)