Results on the Hilbert coefficients and reduction numbers

TL;DR

This paper investigates the properties of Hilbert coefficients and reduction numbers in Cohen-Macaulay local rings, focusing on the independence of reduction ideals and their behavior, supported by illustrative examples.

Contribution

It provides new insights into the independence of reduction ideals and the behavior of higher Hilbert coefficients in Cohen-Macaulay local rings.

Findings

Analysis of the independence of reduction ideals

Behavior of higher Hilbert coefficients examined

Examples illustrating key concepts provided

Abstract

Let $(R,\frak{m})$ be a $d$-dimensional Cohen-Macaulay local ring, $I$ an $\frak{m}$-primary ideal and $J$ a minimal reduction of $I$. In this paper we study the independence of reduction ideals and the behavior of the higher Hilbert coefficients. In addition, we give some examples in this regards.