In particular, we show that if A is of codimension 3, then (hd−1hd)<2(hdhd+1) for every θ<d<s and hs−1≤3hs, and prove that if A is a codimension 3 Artinian algebra with an h-vector (1,3,h2,…,hs) such that
for some r1(A)<d<s, then (Id+1) is (d+1)-regular and .  相似文献   

14.
A note on global pth powers of rigid analytic functions     
Z. Robinson 《Journal of Number Theory》2006,116(2):474-482
Assume that K is a perfect field of characteristic p>0 that is complete with respect to an ultrametric valuation, and let X be a rigid analytic variety over K. Suppose that X is smooth and connected with respect to its Grothendieck topology. Let f be a (global) function on X the differential of which vanishes locally at some point of X; then f is the pth power of a (global) function.  相似文献   

15.
A remark on regularity of powers and products of ideals     
Winfried Bruns  Aldo Conca 《Journal of Pure and Applied Algebra》2017,221(11):2861-2868
We give a simple proof for the fact that the Castelnuovo–Mumford regularity and related invariants of products of powers of ideals are asymptotically linear in the exponents, provided that each ideal is generated by elements of constant degree. We provide examples showing that the asymptotic linearity is false in general. On the other hand, the regularity is always given by the maximum of finitely many linear functions whose coefficients belong to the set of the degrees of generators of the ideals.  相似文献   

16.
Two criteria to check whether ideals are direct sums of cyclically presented modules     
A. Moradzadeh-Dehkordi  S.H. Shojaee 《Journal of Pure and Applied Algebra》2019,223(2):713-720
A famous theorem of commutative algebra due to I. M. Isaacs states that “if every prime ideal of R is principal, then every ideal of R is principal”. Therefore, a natural question of this sort is “whether the same is true if one weakens this condition and studies rings in which ideals are direct sums of cyclically presented modules?” The goal of this paper is to answer this question in the case R is a commutative local ring. We obtain an analogue of Isaacs's theorem. In fact, we give two criteria to check whether every ideal of a commutative local ring R is a direct sum of cyclically presented modules, it suffices to test only the prime ideals or structure of the maximal ideal of R. As a consequence, we obtain: if R is a commutative local ring such that every prime ideal of R is a direct sum of cyclically presented R-modules, then R is a Noetherian ring. Finally, we describe the ideal structure of commutative local rings in which every ideal of R is a direct sum of cyclically presented R-modules.  相似文献   

17.
Embedded associated primes of powers of square-free monomial ideals     
Huy Tài Hà  Susan Morey 《Journal of Pure and Applied Algebra》2010,214(4):301-93
An ideal I in a Noetherian ring R is normally torsion-free if Ass(R/It)=Ass(R/I) for all t≥1. We develop a technique to inductively study normally torsion-free square-free monomial ideals. In particular, we show that if a square-free monomial ideal I is minimally not normally torsion-free then the least power t such that It has embedded primes is bigger than β1, where β1 is the monomial grade of I, which is equal to the matching number of the hypergraph H(I) associated to I. If, in addition, I fails to have the packing property, then embedded primes of It do occur when t=β1+1. As an application, we investigate how these results relate to a conjecture of Conforti and Cornuéjols.  相似文献   

18.
19.
The multiplicity function on exponential and completely solvable homogeneous spaces     
Ronald L. Lipsman 《Geometriae Dedicata》1991,39(2):155-161
It has been shown recently that the same multiplicity function appears in direct integral decompositions of both induced and restricted representations on exponential solvable groups — that is, a generalized form of Frobenius Reciprocity is valid. Qualitative results on that multiplicity function in the completely solvable case are proven in this paper — namely, necessary and sufficient conditions for finiteness and boundedness are obtained. The proof uses techniques from pseudo-algebraic geometry.Research supported by DMS 87-00551A02.  相似文献   

20.
A note on non-reduced Picard schemes     
Christian Liedtke 《Journal of Pure and Applied Algebra》2009,213(5):737-741
The Picard scheme of a smooth curve and a smooth complex variety is reduced. In this note we discuss which classes of surfaces in terms of the Enriques-Kodaira classification can have non-reduced Picard schemes and whether there are restrictions on the characteristic of the ground field. It turns out that non-reduced Picard schemes are uncommon in Kodaira dimension κ≤0, that this phenomenon can be bounded for κ=2 (general type) and that it is as bad as can be for κ=1.  相似文献   

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1.
Inspired by results of Guardo, Van Tuyl and the second author for lines in P3P3, we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r  -dimensional planes in PnPn for n?2r+1n?2r+1. These considerations lead to new conjectures that suggest that the well known conjecture of Nagata for points in P2P2 is not an exotic statement but rather a manifestation of a much more general phenomenon which seems to have been overlooked so far.  相似文献   

2.
Let S be a polynomial ring and I be the Stanley-Reisner ideal of a simplicial complex Δ. The purpose of this paper is investigating the Buchsbaum property of S/I(r) when Δ is pure dimension 1. We shall characterize the Buchsbaumness of S/I(r) in terms of the graphical property of Δ. That is closely related to the characterization of the Cohen-Macaulayness of S/I(r) due to the first author and N.V. Trung.  相似文献   

3.
4.
We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms of the number of its minimal monomial generators and the maximum height of its minimal primes. Received: 12 December 2005  相似文献   

5.
This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gröbner basis can be computed by studying paths in the graph. Since these Gröbner bases are square-free, generalized binomial edge ideals are radical. To find the primary decomposition a combinatorial problem involving the connected components of subgraphs has to be solved. The irreducible components of the solution variety are all rational.  相似文献   

6.
7.
In this paper we characterize all principal Borel ideals with Borel generator up to degree 4 which are Gotzmann. We also classify principal Borel ideals with a Borel generator of degree d which are lexsegment and we describe the shadows of principal Borel ideals. Finally, we discuss the corresponding results for squarefree monomial ideals.Received: 10 May 2002  相似文献   

8.
We prove some results on projective generation of ideals.  相似文献   

9.
We study the set of Cohen-Macaulay monomial ideals with a given radical. Among this set of ideals are the so-called Cohen-Macaulay modifications. Not all Cohen-Macaulay squarefree monomial ideals admit nontrivial Cohen-Macaulay modifications. It is shown that if there exists one such modification, then there exist indeed infinitely many.  相似文献   

10.
In this paper we discuss four different constructions of vector space bases associated to vanishing ideals of points. We show how to compute normal forms with respect to these bases and give new complexity bounds. As an application, we drastically improve the computational algebra approach to the reverse engineering of gene regulatory networks.  相似文献   

11.
12.
In this paper, we use the tools of Gröbner bases and combinatorial secant varieties to study the determinantal ideals It of the extended Hankel matrices. Denote by c-chain a sequence a1,…,ak with ai+c<ai+1 for all i=1,…,k−1. Using the results of c-chain, we solve the membership problem for the symbolic powers and we compute the primary decomposition of the product It1?Itk of the determinantal ideals. Passing through the initial ideals and algebras we prove that the product It1?Itk has a linear resolution and the multi-homogeneous Rees algebra is defined by a Gröbner basis of quadrics.  相似文献   

13.
We find a sufficient condition that is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function cannot be level if hd≤2d+3, and that there exists a level O-sequence of codimension 3 of type for hd≥2d+k for k≥4. Furthermore, we show that is not level if , and also prove that any codimension 3 Artinian graded algebra A=R/I cannot be level if . In this case, the Hilbert function of A does not have to satisfy the condition hd−1>hd=hd+1.Moreover, we show that every codimension n graded Artinian level algebra having the Weak-Lefschetz Property has a strictly unimodal Hilbert function having a growth condition on (hd−1hd)≤(n−1)(hdhd+1) for every d>θ where
h0<h1<<hα==hθ>>hs−1>hs.
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