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2018 A note on quasi-monic polynomials and efficient generation of ideals
Md. Ali Zinna
J. Commut. Algebra 10(3): 411-433 (2018). DOI: 10.1216/JCA-2018-10-3-411

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.

Citation

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Md. Ali Zinna. "A note on quasi-monic polynomials and efficient generation of ideals." J. Commut. Algebra 10 (3) 411 - 433, 2018. https://doi.org/10.1216/JCA-2018-10-3-411

Information

Published: 2018
First available in Project Euclid: 9 November 2018

zbMATH: 06976324
MathSciNet: MR3874661
Digital Object Identifier: 10.1216/JCA-2018-10-3-411

Subjects:
Primary: 13C10, 19A15

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.10 • No. 3 • 2018
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