On the effective reduction of an ideal
Annales Polonici Mathematici
MSC: Primary 13A15; Secondary 13A30, 13B22
DOI: 10.4064/ap240629-19-12
Published online: 12 January 2026
Abstract
It is well known that the reduction of an $\mathfrak m$-primary ideal $\mathfrak q$ in the Noetherian local ring $(R,\mathfrak m)$ with infinite residue field $R/\mathfrak m$ may be given in the form of a sufficiently general linear combination of its generators. We give a condition for the existence of such a reduction in terms of the sum of the degrees of the prime divisors of the ideal fiber cone $\mathcal F_{\mathfrak q}(R)$ in the case of any Noetherian local ring.
