Geodesic
On the number of generators of ideals in polynomial rings
Jean Fasel1
1 Institut Fourier, Université Grenoble Alpes, Grenoble, France
Annals of mathematics, Tome 184 (2016) no. 1, pp. 315-331.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For an ideal $I$ in a noetherian ring $R$, let $\mu(I)$ be the minimal number of generators of $I$. It is well known that there is a sequence of inequalities $\mu(I/I^2)\leq \mu(I)\leq \mu(I/I^2)+1$ that are strict in general. However, Murthy conjectured in 1975 that $\mu(I/I^2)=\mu(I)$ for ideals in polynomial rings whose height equals $\mu(I/I^2)$. The purpose of this article is to prove a stronger form of the conjecture in case the base field is infinite of characteristic different from $2$: Namely, the equality $\mu(I/I^2)=\mu(I)$ holds for any ideal $I$, irrespective of its height.
DOI : 10.4007/annals.2016.184.1.3

Jean Fasel 1

1 Institut Fourier, Université Grenoble Alpes, Grenoble, France 
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Jean Fasel. On the number of generators of ideals in polynomial rings. Annals of mathematics, Tome 184 (2016) no. 1, pp. 315-331. doi : 10.4007/annals.2016.184.1.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.184.1.3/

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