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2.
In an earlier work, the authors described a mechanism for lifting monomial ideals to reduced unions of linear varieties. When the monomial ideal is Cohen–Macaulay (including Artinian), the corresponding union of linear varieties is arithmetically Cohen–Macaulay. The first main result of this paper is that if the monomial ideal is Artinian then the corresponding union is in the Gorenstein linkage class of a complete intersection (glicci). This technique has some interesting consequences. For instance, given any ( d + 1)-times differentiable O-sequence H, there is a nondegenerate arithmetically Cohen–Macaulay reduced union of linear varieties with Hilbert function H which is glicci. In other words, any Hilbert function that occurs for arithmetically Cohen–Macaulay schemes in fact occurs among the glicci schemes. This is not true for licci schemes. Modifying our technique, the second main result is that any Cohen–Macaulay Borel-fixed monomial ideal is glicci. As a consequence, all arithmetically Cohen–Macaulay subschemes of projective space are glicci up to flat deformation. 相似文献
3.
An Artin algebra A is said to be CM-finite if there are only finitely many isomorphism classes of indecomposable finitely generated Gorenstein-projective A-modules. Inspired by Auslander's idea on representation dimension, we prove that for 2? n<∞, A is a CM-finite n-Gorenstein algebra if and only if there is a resolving Gorenstein-projective A-module E such that gl.dimEnd Aop( E)? n. 相似文献
4.
Let k be an algebraically closed field of characteristic 0. We give here a complete classification of local commutative, associative, Artinian, Gorenstein k-algebras with unit, up to multiplicity 9. 相似文献
6.
When the base connected cochain DG algebra is cohomologically bounded, it is proved that the difference between the amplitude
of a compact DG module and that of the DG algebra is just the projective dimension of that module. This yields the unboundedness
of the cohomology of non-trivial regular DG algebras.
When A is a regular DG algebra such that H( A) is a Koszul graded algebra, H( A) is proved to have the finite global dimension. And we give an example to illustrate that the global dimension of H( A) may be infinite, if the condition that H( A) is Koszul is weakened to the condition that A is a Koszul DG algebra. For a general regular DG algebra A, we give some equivalent conditions for the Gorensteiness.
For a finite connected DG algebra A, we prove that D c( A) and D c( A
op) admit Auslander-Reiten triangles if and only if A and A
op are Gorenstein DG algebras. When A is a non-trivial regular DG algebra such that H( A) is locally finite, D c( A) does not admit Auslander-Reiten triangles. We turn to study the existence of Auslander-Reiten triangles in D lfb( A) and D lfb ( A
op) instead, when A is a regular DG algebra.
This work was supported by the National Natural Science Foundation of China (Grant No. 10731070) and the Doctorate Foundation
of Ministry of Education of China (Grant No. 20060246003) 相似文献
7.
Let be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by for each module and for each integer . We propose a conjecture asking if for any positive integers and . We prove that this is true provided the associated graded ring of has depth not less than . Furthermore we show that there are only finitely many possibilities for a pair of positive integers for which . 相似文献
8.
In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat and Gorenstein FP-injective dimensions, and show that some characterizations similar to Gorenstein homological dimensions hold for these two dimensions. 相似文献
9.
Given a compressed Artin level algebra A which satisfies certain properties, it is possible to use this algebra to construct a Gorenstein Artin algebra with a nonunimodal Hilbert function. We show how to construct a minimal free resolution for these algebras, using the minimal free resolution of A. 相似文献
10.
For any skewed-gentle algebra, we characterize its indecomposable Gorenstein projective modules explicitly and describe its Cohen–Macaulay Auslander algebra. We prove that skewed-gentle algebras are always Gorenstein, which is independent of the characteristic of the ground field, and the Cohen–Macaulay Auslander algebras of skewed-gentle algebras are also skewed-gentle algebras. 相似文献
11.
In this paper,we shall be concerned with what happens of Gorenstein homological dimensions when certain modifications are made to a ring.The five structural operations addressed later are the formation of excellent extensions,localizations,Morita equivalences,polynomial extensions and power series extensions. 相似文献
12.
In this note we supply an elementary proof of the following well-known theorem of R. Stanley: the -vectors of Gorenstein algebras of codimension 3 are SI-sequences, i.e. are symmetric and the first difference of their first half is an -sequence. 相似文献
14.
Let A and B be Artin R-algebras of finite Cohen-Macaulay type. Then we prove that, if A and B are standard derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent. And we show that Gorenstein projective conjecture is an invariant under standard derived equivalence between Artin R-algebras. 相似文献
16.
设■是阿贝尔范畴,■是■的子范畴.Sather-Wagstaff, Sharif和White引入了Gorenstein子范畴的概念,记为■.我们用■(相应地,■)代表纯投射R-模类(相应地,投射R-模类).本文给出了一类满足条件"■"的环,由此给出了当■是■的子范畴时,■是否包含在■中的一个否定回答.进一步,刻画了包含关系■和■何时成立. 相似文献
17.
Summary Let R be a Cohen-Macaulay ring and I an unmixed ideal of height g which is generically a complete intersection and satisfies I
(n)=I n for all n≥1. Under what conditions will the Rees algebra be Cohen-Macaulay or have good depth? A series of partial answers to this
question is given, relating the Serre condition ( S
r
) of the associated graded ring to the depth of the Rees algebra. A useful device in arguments of this nature is the canonical
module of the Rees algebra. By making use of the technique of the fundamental divisor, it is shown that the canonical module
has the expected form: ω
R[It]
≅( t(1− t)
g−2).
The third author was partially supported by the NSF
This article was processed by the author using the LaTex style file cljour1 from Springer-Verlag. 相似文献
18.
Let be an -primary ideal in a Gorenstein local ring (, ) with , and assume that contains a parameter ideal in as a reduction. We say that is a good ideal in if is a Gorenstein ring with . The associated graded ring of is a Gorenstein ring with if and only if . Hence good ideals in our sense are good ones next to the parameter ideals in . A basic theory of good ideals is developed in this paper. We have that is a good ideal in if and only if and . First a criterion for finite-dimensional Gorenstein graded algebras over fields to have nonempty sets of good ideals will be given. Second in the case where we will give a correspondence theorem between the set and the set of certain overrings of . A characterization of good ideals in the case where will be given in terms of the goodness in their powers. Thanks to Kato's Riemann-Roch theorem, we are able to classify the good ideals in two-dimensional Gorenstein rational local rings. As a conclusion we will show that the structure of the set of good ideals in heavily depends on . The set may be empty if , while is necessarily infinite if and contains a field. To analyze this phenomenon we shall explore monomial good ideals in the polynomial ring in three variables over a field . Examples are given to illustrate the theorems. 相似文献
19.
In this article, we study height four graded Gorenstein ideals I in k[ x, y, z, w] such that I 2 is of height one and generated by three quadrics. After a suitable linear change of variables, I ∩ k[ x, y, z] is either Gorenstein or of type two. The former case was studied by Iarrobino and Srinivasan [ 8
Iarrobino , A. ,
Srinivasan , H. ( 2005 ). Artininan Gorenstein algebras of embedding dimension four: components of ? Gor (H) for H = (1, 4, 7,…, 1) . Journal of Pure and Applied Algebra 201 : 62 – 96 .[Crossref], [Web of Science ®] , [Google Scholar]] where they give the structure of the ideal and its resolution. We study the latter case and give the structure of these ideals and their minimal resolution. We also explicitly write the form of the generators of I and the maps in the free resolution of R/ I. 相似文献
20.
We show that over a right coherent left perfect ring R, a complex C of left R-modules is Gorenstein projective if and only if C
m
is Gorenstein projective in R-Mod for all m ∈ ℤ. Basing on this we show that if R is a right coherent left perfect ring then Gpd( C) = sup{Gpd( C
m
)| m ∈ ℤ} where Gpd(−) denotes Gorenstein projective dimension. 相似文献
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