Let A be a finite ring. Werner's conjecture says that N(A)={f(t)is an element of A[t]divided by f(b)=0 for all b is an element of A} is a two-sided ideal of A[t] (Werner, N. J. (2014)). We enlarge the scope of this conjecture and prove it under some conditions. In particular, we show that the conjecture is true for N(A,sigma,delta)={f(t)is an element of A[t;sigma,delta]divided by f(b)=0 for all b is an element of A} , where A is a ring whose elements are finite sums of units. We also consider the case of multivariate Ore extensions and conclude the paper with the case of polynomial rings A[t] , where A is a prime ring.