Timeline for Elementary proof that $\operatorname{Ass}(I^n)$ stabilizes for a monomial ideal $I$
Current License: CC BY-SA 3.0
7 events
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Jul 29, 2013 at 10:21 | comment | added | Arno Nym | Actually, nevermind. Looking again at the paper by Ratliff I found that I was basically looking for so called "superficial elements", and the book "Integral Closure of Ideals, Rings and Modules" (Swanson, Huneke) has a proof for existence of superficial elements which only depends on primary decomposition and graded prime avoidance. So I'll go with that one. | |
S Jul 28, 2013 at 15:56 | history | suggested | user26857 | CC BY-SA 3.0 |
small improvements
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Jul 28, 2013 at 15:53 | review | Suggested edits | |||
S Jul 28, 2013 at 15:56 | |||||
Jul 27, 2013 at 2:05 | comment | added | Arno Nym | Hm. Maybe you could help me understand the proof of Remark 1(b) in McAdam's paper. It says there's a $t \geq 1$ such that $(I^{n+1} : I) \cap I^t = I^n$ for $n \geq t$. The proof uses the form ring of I. I'd like to "translate" that proof so there's no mention of "homogeneous Noetherian ring" or any of that wizardry. Basically I got as far as defining $B_k$ as the set of monomials in $(I^{k+2} : I) \cap I^k - I^{k+1}$ and define $B$ as the monomial ideal generated by the union of the $B_k$. I'm pretty sure B corresponds to McAdam's $(0:R_1)$ somehow, but I'm not sure how to finish from there. | |
Jul 25, 2013 at 20:49 | comment | added | Dietrich Burde | Perhaps the bachelor thesis would even benefit from including "the language of graded rings". The result is Corollary 5 in the McAdam paper, and the proof seems accessible. | |
Jul 25, 2013 at 13:48 | review | First posts | |||
Jul 25, 2013 at 13:50 | |||||
Jul 25, 2013 at 13:30 | history | asked | Arno Nym | CC BY-SA 3.0 |