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1.
We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obner basis of the ideal. Further we give a projective analogue for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre's inequality for the number of points of projective hypersurfaces over finite fields is included. 相似文献
2.
We study finitely generated modules M over a ring R, noetherianon both sides. If M has finite Gorenstein dimension G-dimRMin the sense of Auslander and Bridger, then it determines twoother cohomology theories besides the one given by the absolutecohomology functors . Relative cohomology functors are defined for all non-negative integers n; they treat the modules of Gorensteindimension 0 as projectives and vanish for n > G-dimRM. Tatecohomology functors are defined for all integers n; all groups vanish if M or N has finite projective dimension. Comparisonmorphisms and link these functors. We give a self-contained treatmentof modules of finite G-dimension, establish basic propertiesof relative and Tate cohomology, and embed the comparison morphismsinto a canonical long exact sequence . We show that these results provide efficient tools for computingold and new numerical invariants of modules over commutativelocal rings. 2000 Mathematical Subject Classification: 16E05, 13H10, 18G25. 相似文献
3.
文 [1],[2 ]分别研究了Gr NoetherGr 局部 (半局部 )环的同调维数 ,本文主要进一步讨论Gr 凝聚Gr 半局部环的同调性质 .在§ 1中 ,主要刻画交换Gr 凝聚Gr 半局部环R的分次弱整体维数gr.gl.w .dimR ;在§ 2中 ,定义了分次环R的小有限分次投射维数gr.fp .dimR .刻画了gr.fp .dimR =gr .gl.w .dimR的Gr 凝聚环 .由于Gr Noether环是Gr 凝聚的 ,因而本文所得的结果对于Gr Noether环是自然成立的 .同时 ,本文所得的结果 ,也可视为文 [4 ]关于一般交换凝聚环相应结论的推广 . 相似文献
4.
Maria Vaz Pinto 《代数通讯》2013,41(9):3376-3396
Let X* be a subset of an affine space 𝔸 s , over a finite field K, which is parameterized by the edges of a clutter. Let X and Y be the images of X* under the maps x → [x] and x → [(x, 1)], respectively, where [x] and [(x, 1)] are points in the projective spaces ? s?1 and ? s , respectively. For certain clutters and for connected graphs, we were able to relate the algebraic invariants and properties of the vanishing ideals I(X) and I(Y). In a number of interesting cases, we compute its degree and regularity. For Hamiltonian bipartite graphs, we show the Eisenbud–Goto regularity conjecture. We give optimal bounds for the regularity when the graph is bipartite. It is shown that X* is an affine torus if and only if I(Y) is a complete intersection. We present some applications to coding theory and show some bounds for the minimum distance of parameterized linear codes for connected bipartite graphs. 相似文献
5.
Finite Projective Geometries and Classification of the Weight Hierarchies of Codes (Ⅰ) 总被引:1,自引:0,他引:1
WenDeCHEN TorleivKLφVE 《数学学报(英文版)》2004,20(2):333-348
The weight hierarchy of a binary linear [n,κ] code C is the sequence (d1,d2,...,dκ), where dr is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries.The possible weight hierarchies in class A, B, C, D are determined in Part (Ⅰ). The possible weight hierarchies in class E, F, G, H, I are determined in Part (Ⅱ). 相似文献
6.
The flag geometry Γ=(
,
, I) of a finite projective plane Π of order s is the generalized hexagon of order (s, 1) obtained from Π by putting
equal to the set of all flags of Π, by putting
equal to the set of all points and lines of Π, and where I is the natural incidence relation (inverse containment), i.e., Γ is the dual of the double of Π in the sense of H. Van Maldeghem (1998, “Generalized Polygons,” Birkhäuser Verlag, Basel). Then we say that Γ is fully and weakly embedded in the finite projective space PG(d, q) if Γ is a subgeometry of the natural point-line geometry associated with PG(d, q), if s=q, if the set of points of Γ generates PG(d, q), and if the set of points of Γ not opposite any given point of Γ does not generate PG(d, q). In two earlier papers we have shown that the dimension d of the projective space belongs to {6, 7, 8}, that the projective plane Π is Desarguesian, and we have classified the full and weak embeddings of Γ (Γ as above) in the case that there are two opposite lines L, M of Γ with the property that the subspace UL, M of PG(d, q) generated by all lines of Γ meeting either L or M has dimension 6 (which is automatically satisfied if d=6). In the present paper, we partly handle the case d=7; more precisely, we consider for d=7 the case where for all pairs (L, M) of opposite lines of Γ, the subspace UL, M has dimension 7 and where there exist four lines concurrent with L contained in a 4-dimensional subspace of PG(7, q). 相似文献
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8.
In this article, we characterize several properties of commutative noetherian local rings in terms of the left perpendicular category of the category of finitely generated modules of finite projective dimension. As an application, we prove that a local ring is regular if (and only if) there exists a strong test module for projectivity having finite projective dimension. We also obtain corresponding results with respect to a semidualizing module. 相似文献
10.
A. V. Tsarev 《Mathematical Notes》2006,80(3-4):417-427
The projective, flat, and generating modules over the ring of pseudorational numbers are described. For the projective modules, a complete independent system of invariants is constructed. 相似文献
11.
《Mathematische Nachrichten》2018,291(1):28-40
We study the equality of the extremal Betti numbers of the binomial edge ideal and those of its initial ideal for a closed graph G. We prove that in some cases there is a unique extremal Betti number for and as a consequence there is a unique extremal Betti number for and these extremal Betti numbers are equal. 相似文献
12.
Moshe Roitman 《代数通讯》2015,43(1):337-344
We present a simplified proof of Arnold's Theorem on the SFT property and the dimension of power series rings. 相似文献
13.
Let Abe an affine domain of dimension nover an algebraically closed field kof characteristic 0. Let I A[T]be a local complete intersection ideal of height nsuch that I/I2 is generated by n elements. It is proved that there exists a projective A[T]module Pof rank nsuch that Iis a surjective image of P. 相似文献
14.
David G. Glynn 《Geometriae Dedicata》1997,66(3):343-355
The classification of cone-representations of projective planes of orderq
3 of index 3 and rank 4 (and so in PG(6,q)) is completed. Any projective plane with a non-spread representation (being a cone-representation of the second kind) is a dual generalised Desarguesian translation plane, as found by Jha and Johnson, and conversely. Indeed, given any collineation of PG(2,q) with no fixed points, there exists such a projective plane of order q3 , where q is a prime power, that has the second kind of cone-representation of index 3 and rank 4 in PG(6,q). An associated semifield plane of order q
3 is also constructed at most points of the plane. Although Jha and Johnson found this plane before, here we can show directly the geometrical connection between these two kinds of planes. 相似文献
15.
In this note we consider the set of incidence matrices of a cyclic projective planes whose set of points has cardinality a prime number p. We provide a correct proof of a result of Ho, showing that there exists an incidence matrix that possesses exactly p distinct eigenvalues. 相似文献
16.
Graph G is a (k, p)‐graph if G does not contain a complete graph on k vertices Kk, nor an independent set of order p. Given a (k, p)‐graph G and a (k, q)‐graph H, such that G and H contain an induced subgraph isomorphic to some Kk?1‐free graph M, we construct a (k, p + q ? 1)‐graph on n(G) + n(H) + n(M) vertices. This implies that R (k, p + q ? 1) ≥ R (k, p) + R (k, q) + n(M) ? 1, where R (s, t) is the classical two‐color Ramsey number. By applying this construction, and some its generalizations, we improve on 22 lower bounds for R (s, t), for various specific values of s and t. In particular, we obtain the following new lower bounds: R (4, 15) ≥ 153, R (6, 7) ≥ 111, R (6, 11) ≥ 253, R (7, 12) ≥ 416, and R (8, 13) ≥ 635. Most of the results did not require any use of computer algorithms. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 231–239, 2004 相似文献
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19.
We denote by 𝒜(R) the class of all Artinian R-modules and by 𝒩(R) the class of all Noetherian R-modules. It is shown that 𝒜(R) ? 𝒩(R) (𝒩(R) ? 𝒜(R)) if and only if 𝒜(R/P) ? 𝒩(R/P) (𝒩(R/P) ? 𝒜(R/P)), for all centrally prime ideals P (i.e., ab ∈ P, a or b in the center of R, then a ∈ P or b ∈ P). Equivalently, if and only if 𝒜(R/P) ? 𝒩(R/P) (𝒩(R/P) ? 𝒜(R/P)) for all normal prime ideals P of R (i.e., ab ∈ P, a, b normalize R, then a ∈ P or b ∈ P). We observe that finitely embedded modules and Artinian modules coincide over Noetherian duo rings. Consequently, 𝒜(R) ? 𝒩(R) implies that 𝒩(R) = 𝒜(R), where R is a duo ring. For a ring R, we prove that 𝒩(R) = 𝒜(R) if and only if the coincidence in the title occurs. Finally, if Q is the quotient field of a discrete valuation domain R, it is shown that Q is the only R-module which is both α-atomic and β-critical for some ordinals α,β ≥ 1 and in fact α = β = 1. 相似文献
20.
D. Juriev 《Acta Appl Math》1998,50(1-2):191-196
This paper is a revised and expanded version of two notes devoted to nonassociative structures in quantum projective field theory. 相似文献