منابع مشابه
Derivations and bounded nilpotence index
We construct a nil ring R which has bounded index of nilpotence 2, is Wedderburn radical, and is commutative, and which also has a derivation δ for which the differential polynomial ring R[x; δ] is not even prime radical. This example gives a strong barrier to lifting certain radical properties from rings to differential polynomial rings. It also demarcates the strength of recent results about ...
متن کاملCoproducts and the Cd-index *
Dedicated to Gian-Carlo Rota on his 2 6 th birthday. Abstract The linear span of isomorphism classes of posets, P, has a Newtonian coalgebra structure. We observe that the ab-index is a Newtonian coalgebra map from the vector space P to the algebra of polynomials in the non-commutative variables a and b. This enables us to obtain explicit formulas showing how the cd-index of the face lattice of...
متن کاملCoproducts and the cd-Index
The linear span of isomorphism classes of posets, P, has a Newtonian coalgebra structure. We observe that the ab-index is a Newtonian coalgebra map from the vector space P to the algebra of polynomials in the non-commutative variables a and b. This enables us to obtain explicit formulas showing how the cd-index of the face lattice of a convex polytope changes when taking the pyramid and the pri...
متن کاملThe Cd-index of Fans and Lattices
where hk = dim(A(∆)⊗AR) k. When the fan ∆ is rational, it corresponds to a toric variety X(∆) and the numbers hk are the even betti numbers of the cohomology of X(∆). In any case, they satisfy the Poincaré duality hk = hn−k. When the fan ∆ is complete but not necessarily simplicial, one can apply the same construction to the first barycentric subdivision B(∆) of ∆. We can label a 1-dimensional ...
متن کاملThe cd-index of zonotopes and arrangements
We investigate a special class of polytopes, the zonotopes, and show that their flag f -vectors satisfy only the affine relations fulfilled by flag f -vectors of all polytopes. In addition, we determine the lattice spanned by flag f -vectors of zonotopes. By duality, these results apply as well to the flag f -vectors of central arrangements of hyperplanes.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2008
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-008-9067-9