A note on quasi-monic polynomials and efficient generation of ideals. (English) Zbl 1427.13010

Summary: Let \(A\) be a commutative Noetherian ring, and let \(I\) be an ideal of \(A[T]\) containing a quasi-monic polynomial. Assuming that \(I/I^2\) is generated by \(n\) elements, where \(n\geq \dim (A[T]/I)+2\), then, it is proven that any given set of \(n\) generators of \(I/I^2\) can be lifted to a set of \(n\) generators of \(I\). It is also shown that various types of Horrocks’ type results (previously proven for monic polynomials) can be generalized to the setting of quasi-monic polynomials.


13C10 Projective and free modules and ideals in commutative rings
19A15 Efficient generation of modules
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