Sally modules of rank one

TL;DR

This paper investigates the structure of Sally modules associated with certain $km$-primary ideals in Cohen-Macaulay local rings, focusing on cases where the first two Hilbert coefficients satisfy a specific equality, revealing new structural insights.

Contribution

It provides a detailed analysis of Sally modules of rank one under a particular Hilbert coefficient condition, offering new structural characterizations.

Findings

Characterization of Sally modules when $ ext{e}_1(I)= ext{e}_0(I)- ext{length}_A(A/I)+1$

Structural properties of Sally modules of rank one in Cohen-Macaulay rings

Insights into the Hilbert coefficients' influence on Sally module structure

Abstract

The structure of Sally modules of $\fkm$-primary ideals $I$ in a Cohen-Macaulay local ring $(A, \m)$ satisfying the equality $\e_1(I)=\e_0(I)-\ell_A(A/I)+1$ is explored, where $\e_0(I)$ and $\e_1(I)$ denote the first two Hilbert coefficients of $I$.