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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
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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