## 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.

### MSC:

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

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