Sections of zero dimensional ideals over a Noetherian ring (Q2642849)

Let \(A\) be a commutative noetherian ring with identity. For an ideal \(I\) of the polynomial ring \(A[T]\), write \(I(0)=\{f(0):f\in I\}.\) Suppose that \(I\) contains a monic polynomial and that \(A[T]/I\) is zero dimensional dimensional. The author shows that if the conormal module \(I/I^{2}\) is generated over \(A[T]/I\) by \(r\) elements and if \(r\geq 2\), then a set of \(r\) generators of \(I(0)\) can be lifted to a set of \(r\) generators of \(I.\) The motivation for the author's work comes from the work of \textit{S. Mandal} [Invent. Math. 75, 59--67 (1984; Zbl 0513.13006)]. The same result in the semi-local case was proved by the author and \textit{S. Mandal} [J. Pure Appl. Algebra 169, No. 1, 29--32 (2002; Zbl 1067.13012)].