What polynomial satisfies a given endomorphism? (Q1805219)

Let \(R\) be a commutative ring with unit, \(M\) a finitely generated \(R\)- module, and \(u\) an endomorphism of \(M\). Let \(I(u) = \{p(X) \in R[X] : p(u) = 0\}\) be the ideal of relations satisfied by \(u\). The paper concerns the problem of determining the ideal \(I(u)\) in the case \(M\) has a finite free resolution. The results generalize the classical case \(R = k\) (\(k\) is a field) and the results of \textit{N. H. McCoy} [Bull. Am. Math. Soc. 45, 280-284 (1939; Zbl 0021.00404)] in the case \(M\) is a finite free \(R\)-module.