Kernel coefficient ideals in Noetherian rings (Q1911320)

Let \(b_1, \dots, b_n\) be a minimal basis of an ideal \(I\) in a noetherian ring \(R\), \(f:R[X_1, \dots, X_n] \to R[t]\) the \(R\)-morphism given by \(X_i\to tb_i\). Then the ideal \(I^*\) (called the kernel coefficient ideal) generated in \(R\) by the coefficients of the polynomials in \(\text{Ker} f\) depends actually only on \(I\). Many nice properties of such ideals \(I^*\) are given. They behave somehow like the ideals generated by \(R\)-sequences. If \(J,L\) are other ideals of \(R\) and \(I^*\subset J\cap L\) then \(((I^*)^sJ: (I^*)s)=J\), \(I^*(J\cap L)= I^*J\cap I^* L\), \(\text{Ass} (R/I)\subset \text{Ass} (R/(I^*)^s J)\subset \text{Ass} (R/(I^*)^s) \cup \text{Ass} (R/J)\) for all \(s>1\) and \(J\subset L\) if \(I^*J\subset I^*L\).