## Journal of Commutative Algebra

### A note on quasi-monic polynomials and efficient generation of ideals

Md. Ali Zinna

#### Abstract

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.

#### Article information

Source
J. Commut. Algebra, Volume 10, Number 3 (2018), 411-433.

Dates
First available in Project Euclid: 9 November 2018

https://projecteuclid.org/euclid.jca/1541754168

Digital Object Identifier
doi:10.1216/JCA-2018-10-3-411

Mathematical Reviews number (MathSciNet)
MR3874661

Zentralblatt MATH identifier
06976324

#### Citation

Zinna, Md. Ali. A note on quasi-monic polynomials and efficient generation of ideals. J. Commut. Algebra 10 (2018), no. 3, 411--433. doi:10.1216/JCA-2018-10-3-411. https://projecteuclid.org/euclid.jca/1541754168

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