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# Stephen Sturgeon

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## Registered User

 Name Stephen Sturgeon Member for 1 year Seen 10 hours ago Website Location Age
 May23 accepted Connection between the number of vertices and the number of lattice points of the integer hull of a polytope? May22 answered Connection between the number of vertices and the number of lattice points of the integer hull of a polytope? May22 comment identity for number of monomialsCould you give a small example of $b(n,k)$ and the associated monomials in some small case? May22 comment Computational Ring Theory Macaulay2 is also good software for commutative rings. May22 answered local complete intersection May22 accepted Upper bound of a series May21 answered Upper bound of a series May20 answered Real root of a cubic equation May20 accepted An example of a ring $R$ with the property that for each $P=Ann_R(r)\in {\rm Min}(R)$ we have $Ann_R(P)=Rr$. May15 comment Is there a name for this graph?What is wrong with calling it the Hasse diagram of the inclusion poset? May14 answered How to find overlap between two convex hulls,along with the overlap area May13 comment ideals of a noetherian ring $R$ Cohen-Macaulay as $R-$modulesYou will at least need to look outside of the polynomial ring. No ideals are Cohen-Macaulay as $k[x_1,...,x_n]$ modules by Boij-S\"oderberg decomposition. May13 awarded ● Editor May13 revised An example of a ring $R$ with the property that for each $P=Ann_R(r)\in {\rm Min}(R)$ we have $Ann_R(P)=Rr$.added 7 characters in body May13 comment An example of a ring $R$ with the property that for each $P=Ann_R(r)\in {\rm Min}(R)$ we have $Ann_R(P)=Rr$.Consider $R=k[x,y]/(xy)$. Then R is just the vector space spanned by $(1,x,x^2,...,y,y^2,...)$ because any mixed terms of $xy$ will be eliminated. Thus we can calculate the annihilator by considering products of things in this basis. $x^i*y^j=0$ where as all other products just give a power of a variable. Hence the annihilators are proven. We note that $(x)$ and $(y)$ are the minimal primes. Then $(x) \subset (x,y) \subset R$ is a maximal chain of primes so the dimension is 1. May13 answered An example of a ring $R$ with the property that for each $P=Ann_R(r)\in {\rm Min}(R)$ we have $Ann_R(P)=Rr$. Apr27 awarded ● Scholar Apr27 accepted Secondary Polytope Simplicial? Apr25 awarded ● Teacher Apr25 answered Secondary Polytope Simplicial? Apr25 comment Secondary Polytope Simplicial?I apologize for the confusion. The secondary polytope of an n-gon is the associahedron, which is simple not simplicial. By duality I can always study the dual simplicial polytope in this situation. My question should be rephrased as "Is the secondary polytope always either simple or simplicial?" Apr23 asked Secondary Polytope Simplicial?