Invariance of a length associated to a reduction

Abstract

Let $(A,\mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring with infinite residue field and let $J$ be a minimal reduction of $\mathfrak{m}$. We show that $\lambda ({\mathfrak{m}}^3/J{\mathfrak{m}}^2)$ is independent of $J$.

3 pages. Accepted for publication in Communications in Algebra