The structure of Sally modules and Buchsbaumness of associated graded rings

Abstract

Let $A$ be a Noetherian local ring with the maximal ideal $\mathfrak{m}$, and let $I$ be an $\mathfrak{m}$-primary ideal in $A$. This paper examines the equality on Hilbert coefficients of $I$ first presented by Elias and Valla, but without assuming that $A$ is a Cohen–Macaulay local ring. That equality is related to the Buchsbaumness of the associated graded ring of $I$.