For 'good' monomial ideals, the Ratliff-Rush closure equals the intersection of n ideals obtained by stabilizing along the coordinate axes.
On the number of generators of powers of an ideal
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study the number of generators of ideals in regular rings and ask the question whether $\mu(I)<\mu(I^2)$ if $I$ is not a principal ideal, where $\mu(J)$ denotes the number of generators of an ideal $J$. We provide lower bounds for the number of generators for the powers of an ideal and also show that the CM-type of $I^2$ is $\geq 3$ if $I$ is a monomial ideal of height $n$ in $K[x_1,\ldots,x_n]$ and $n\geq 3$.
citation-role summary
background 1
citation-polarity summary
fields
math.AC 1years
2019 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Powers of monomial ideals and the Ratliff-Rush operation
For 'good' monomial ideals, the Ratliff-Rush closure equals the intersection of n ideals obtained by stabilizing along the coordinate axes.