Lifting of generators of ideals to Laurent polynomial ring (Q1943348)

The authors prove some results about the lifting of generators of an ideal to the Laurent polynomial ring analogous to the polynomial ring. In the main result, they show that for an ideal \(I\) of \(A[T, T^{-1}]\) containing a doubly monic polynomial and \(\mu(I/I^2)= r\geq \dim(A[T, T^{-1}]/I)+2, I(1)= \langle a_1,\dots,a_r\rangle\subseteq \mathrm{Rad}(A)\) and if \(I(1)\) is a complete intersection ideal of height \(r\), then there exists a generating set \(\{f_1,\dots,f_r\}\) of \(I\) such that \(f_i(1)=a_i\), for \(i \in \{1,\dots,r\}\).