منابع مشابه
Polytopal Linear Groups
The main objects of this paper are the graded automorphisms of w x polytopal semigroup rings, i.e., semigroup rings k S where k is a field P Ž and S is the semigroup associated with a lattice polytope P Bruns, P w x. w x Gubeladze, and Trung BGT . The generators of k S correspond bijecP tively to the lattice points in P, and their relations are the binomials representing the affine dependencies...
متن کاملPolytopal Linear Retractions
We investigate graded retracts of polytopal algebras (essentially the homogeneous rings of affine cones over projective toric varieties) as polytopal analogues of vector spaces. In many cases we show that these retracts are again polytopal algebras and that codimension 1 retractions factor through retractions preserving the semigroup structure. We expect that these results hold in general. This...
متن کاملPolytopal Linear Algebra
We investigate similarities between the category of vector spaces and that of polytopal algebras, containing the former as a full subcategory. In Section 2 we introduce the notion of a polytopal Picard group and show that it is trivial for fields. The coincidence of this group with the ordinary Picard group for general rings remains an open question. In Section 3 we survey some of the previous ...
متن کاملNSE characterization of some linear groups
For a finite group $G$, let $nse(G)={m_kmid kinpi_e(G)}$, where $m_k$ is the number of elements of order $k$ in $G$ and $pi_{e}(G)$ is the set of element orders of $G$. In this paper, we prove that $Gcong L_m(2)$ if and only if $pmid |G|$ and $nse(G)=nse(L_m(2))$, where $min {n,n+1}$ and $2^n-1=p$ is a prime number.
متن کاملA Polytopal Generalization of Sperner's Lemma
We prove the following conjecture of Atanassov (Studia Sci. Math. Hungar. 32 (1996), 71–74). Let T be a triangulation of a d-dimensional polytope P with n vertices v1; v2; . . . ; vn: Label the vertices of T by 1; 2; . . . ; n in such a way that a vertex of T belonging to the interior of a face F of P can only be labelled by j if vj is on F : Then there are at least n d full dimensional simplic...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7831