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Gorenstein范畴上的一个问题
纯投射模 Gorenstein投射模 Gorenstein范畴
2019/4/17
设A是阿贝尔范畴，X是A的子范畴.Sather-Wagstaff，Sharif和White引入了Gorenstein子范畴的概念，记为G（X）.我们用PP（相应地，P）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“G（P）⊆G（PP）”的环，由此给出了当W是X的子范畴时，G（W）是否包含在G（X）中的一个否定回答.进一步，刻画了包含关系G（P）⊆G（P...
相对Gorenstein投射模
相对Gorenstein投射模 相对整体维数 相对可解
2018/2/6
设环$A$是环$B$的扩张环,即$B$是与$A$有相同单位的$A$的子环. 记$\mathcal P(A,B)$是由所有相对投射模构成的范畴.对于扩张$B\hookrightarrow A$, 本文介绍相对Gorenstein投射模的概念.由于Gorenstein投射模与投射模具有紧密的联系,并且关于Gorenstein维数有较好的性质,本文想给出相对Gorenstein投射模和相对投射模之间类似...
Sperner property and finite-dimensional Gorenstein algebras associated to matroids
Sperner property finite-dimensional Gorenstein algebras matroids Commutative Algebra
2011/9/21
Abstract: We prove the Lefschetz property for a certain class of finite-dimensional Gorenstein algebras associated to matroids. Our result implies the Sperner property of the vector space lattice. We ...
$n$-strongly Gorenstein rings
strongly (n-)Gorenstein projective injective modules Gorenstein global dimensions
2011/8/24
Abstract: This paper introduces and studies a particular subclass of the class of commutative rings with finite Gorenstein global dimension.
Gorenstein isolated quotient singularities over C
Gorenstein isolated quotient singularities
2011/1/21
In this paper we review the classification of isolated quotient singularities over the field of complex numbers due to H. Zassenhaus,G. Vincent, and J. A. Wolf. As an application we describe Gorenstei...
Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes
secant variety catalecticant minors Veronese variety Veronese reembeddings
2011/2/21
We study the secant varieties of the Veronese varieties and of Veronese reembeddings of a smooth projective variety.
On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension Four
Hilbert Functions Gorenstein Artin Algebras
2010/11/18
We prove that the Hilbert functions of codimension four graded Gorenstein Artin algebras R/I are unimodal provided I has a minimal generator in degree less than five. It is an open question whether al...
Gorenstein投射模
Gorenstein投射模 Gorenstein代数 逼近
2009/12/23
本文简要概述Gorenstein同调代数中最基本的概念、结果、典型的证明以及最近的若干进展。
紧致DG模和Gorenstein DG代数
微分分次代数 Gorenstein微分分次代数 正则微分分次代数 Koszul微分分次代数 紧致微分分次模 Auslander-Reiten三角 amplitude\quad 投射维数
2009/8/31
证明同调有界的连通微分分次代数(简称为DG代数)上的紧致DG模的amplitude与基代数的amplitude的差恰为该DG模的投射维数. 由此可得非平凡的正则DG代数是同调无界的. 对正则DG代数$A$, 若它的同调代数$H(A)$是分次Koszul代数, 则证明$H(A)$有有限的整体维数; 如果把条件减弱为$A$是Koszul DG代数, 则给出了一个$H(A)$的整体维数为无限的例子. 对...
Auslander－Gorenstein滤环上的全律模
Auslander－Gorenstein滤环 全律模 特征簇
2007/12/12
本文给出了Ａｕｓｌａｎｄｅｒ－Ｇｏｒｅｎｓｔｅｉｎ滤环上全律模（ｈｏｌｏｎｏｍｉｃｍｏｄｕｌｅｓ）的一个特征簇刻划，由此得到了通过特征理想的极小素因子（有限个）计算余维数的公式。
Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U _{\Gamma}$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with resp...