2 problems

Let $(R,\mathfrak{m})$ be a Noetherian local ring of dimension $d$, and let $I$ and $J$ be $\mathfrak{m}$-primary ideals. For $0\leq i\leq d$, let $e_i(I\mid J)$ denote their mixed…

Let $(R,\mathfrak{m})$ be a Noetherian local ring of dimension $d\geq2$, and let $I$ and $J$ be $\mathfrak{m}$-primary ideals. Define $e_i=e_i(I\mid J)$ for $0\leq i\leq d$. Teissi…