Graham Leuschke
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Registered User
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15h |
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Canonical Modules That is a hypersurface ring, so Gorenstein, so the canonical module is the ring itself. |
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May 14 |
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ideals of a noetherian ring $R$ Cohen-Macaulay as $R-$modules The length of a maximal $R$-sequence in $P$ is usually denoted $\mathrm{depth}_P(R)$, while $\mathrm{depth}_R(P)$ would mean the length of a maximal $P$-sequence in $R$. Also, it's not true in general that $\mathrm{depth}_R(M) = \mathrm{depth}_R(\mathrm{Ann}_R(M))$; for example, if $R$ is a domain then $\mathrm{depth}_R(R) \geq 1$, while $\mathrm{depth}_R(\mathrm{Ann}_R(R))=0$. |
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May 13 |
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ideals of a noetherian ring $R$ Cohen-Macaulay as $R-$modules I think it's a cut-n-paste error, perhaps supposed to be $\mathrm{depth}_R(P) = \mathrm{dim}(R)$. In that case, $P$ must have height (at most) $1$ and $R/P$ must be a CM ring. |
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May 13 |
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An example of a ring $R$ with the property that for each $P=Ann_R(r)\in {\rm Min}(R)$ we have $Ann_R(P)=Rr$. More generally, any reduced Gorenstein local ring of dimension one will satisfy this double-annihilator property. |
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May 13 |
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An example of a ring $R$ with the property that for each $P=Ann_R(r)\in {\rm Min}(R)$ we have $Ann_R(P)=Rr$. You can localize at the ideal $(x,y)$ to get a local example. |
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May 8 |
accepted | Height unmixed ideal |
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May 7 |
answered | Height unmixed ideal |
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May 7 |
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When does “second annihilator” of a (principal) ideal equal the ideal itself , ie $Ann_R(Ann_R(r))=Rr$? $R=\Bbb {Z}/n\Bbb {Z}$ is itself an artinian Gorenstein ring. |
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Apr 25 |
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Central Element in Sklyanin Algebras? If translation by the point $\tau$ of the elliptic curve $E$ has infinite order, then the center of $A$ is $k[g]$. That's the only intrinsic description of $g$ I know. There might be more known about the two central elements in the Sklyanin algebra of GKdim 4. Paul Smith has some notes that might be useful there: math.washington.edu/~smith/Research/… |
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Apr 22 |
awarded | ● Popular Question |
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Apr 21 |
awarded | ● Good Question |
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Apr 9 |
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$k[[x]]$ as a $(k[[x]])^p$ module for ugly fields Oops, it's not. I should have said 'flat', which Karl already noted in the question. |
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Apr 9 |
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$k[[x]]$ as a $(k[[x]])^p$ module for ugly fields I guess it's a direct limit of free modules, so at least projective. |
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Mar 31 |
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Notation Problem, Fixed Rings and Fields Links for the lazy: citeseerx.ist.psu.edu/viewdoc/… and www-apr.lip6.fr/~avb/DonneesTelechargeables/…, respectively. |
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Mar 11 |
answered | When does End(M) consist entirely of zero, zero divisors, and units? |
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Mar 8 |
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On the equation defining a surface display |
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Mar 2 |
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Detecting and counting free direct summands Entirely possible I'm missing something silly. |
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Mar 2 |
asked | Detecting and counting free direct summands |
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Feb 20 |
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Question in the paper of Robert Bryant “Calibrated embeddings in the special Lagrangian and coassociative cases” backticks |
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Feb 18 |
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How to check if a commutative ring is Gorenstein. Dear Sándor, of course I was not offended. You're right -- our answers complement each other. In fact, a full list of all the ways to answer this question might involve a pretty broad cross-section of commutative algebra and algebraic geometry. |
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Feb 18 |
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How to check if a commutative ring is Gorenstein. I also wish Sándor [and all people 'like' and 'unlike' him] nothing but long life and happiness, but I do want to say that while my first answer is admittedly pretty black-boxy, the second one and Youngsu's comment following are both easy and instructive to do by hand, and that it's only by doing many such examples that we can get the kind of algebraic intuition that serves us [i.e. me] when we [i.e. I] meet examples that are not so susceptible to geometry. |
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Feb 18 |
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How to check if a commutative ring is Gorenstein. Yes, absolutely. |
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Feb 18 |
accepted | How to check if a commutative ring is Gorenstein. |
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Feb 18 |
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How to check if a commutative ring is Gorenstein. added alt. method |
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Feb 18 |
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How to check if a commutative ring is Gorenstein. added 49 characters in body |
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Feb 18 |
answered | How to check if a commutative ring is Gorenstein. |
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Feb 3 |
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Jacobian ideals reference A student of Huneke's named Hsin-Ju Wang wrote some papers about the Jacobian, and always cited Lipman-Sathaye for the definition and basic properties. Here's one of Wang's papers: tandfonline.com/doi/abs/10.1080/00927879808826222 |
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Feb 2 |
revised |
When must it be sets rather than proper classes, or vice-versa, outside of foundational mathematics? backticks again |
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Dec 4 |
revised |
Question on localization technique added 8 characters in body |
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Nov 30 |
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Mutually tangent ellipsoids in 3 space I suspect the asker wanted the interiors of the ellipsoids to be disjoint. |
