2 problems

Let $(R,\mathfrak{m})$ be a Cohen–Macaulay local ring with infinite residue field and dimension at least $2$. A minimal reduction $I$ of $\mathfrak{m}$ is a reduction minimal under…

Let $(R, \mathfrak{m})$ be a Cohen–Macaulay local ring with infinite residue field and … For a minimal reduction $I$ of $\mathfrak{m}$, let $n_3(I)$ denote the asymptotic fullness…