Hilbert-Samuel polynomial
= Hilbert-Samuel polynomial
{c}
For an $\mathfrak m$-primary <ideal> $I$ in a <Noetherian local ring>, $\operatorname{length}(R/I^n)$ agrees for all sufficiently large $n$ with the Hilbert-Samuel <polynomial> of $I$.
= Hilbert-Samuel polynomial
{c}
For an $\mathfrak m$-primary <ideal> $I$ in a <Noetherian local ring>, $\operatorname{length}(R/I^n)$ agrees for all sufficiently large $n$ with the Hilbert-Samuel <polynomial> of $I$.