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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.
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...
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。