结合环的Foxby等价

On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence

Let R be a local ring and C a semidualizing module of R. We investigate the behavior of certain classes of generalized Cohen-Macaulay R-modules under the Foxby equivalence between the Auslander and Bass classes with respect to C. In particular, we show that generalized Cohen-Macaulay R-modules are invariant under this equivalence and if M is a finitely generated R-module in the Auslander class with respect to C such that C\otimes_RM is surjective Buchsbaum, then M is also surjective Buchsbaum.

关于 $C$-$fp_n$-内射与 $C$-$fp_{n}$-平坦模的 Foxby 等价

Foxby equivalence relative to $C$-$fp_n$-injective and $C$-$fp_{n}$-flat modules

本文引入 $C$-$fp_n$-内射与 $C$-$fp_n$-平坦模类，研究其维数、Foxby 等价、预包络与覆盖的存在性，并在几乎优扩张下探讨其交换性质。

Foxby equivalence, local duality and Gorenstein homological dimensions

Let $(R,\fm)$ be a local ring and $(-)^{\vee}$ denote the Matlis duality functor. We investigate the relationship between Foxby equivalence and local duality through generalized local cohomology modules. Assume that $R$ possesses a normalized dualizing complex $D$ and $X$ and $Y$ are two homologically bounded complexes of $R$-modules with finitely generated homology modules. We present several duality results for $\fm$-section complex ${\bf R}Γ_{\fm}({\bf R}\Hom_R(X,Y))$. In particular, if G-dimension of $X$ and injective dimension of $Y$ are finite, then we show that $${\bf R}Γ_{\fm}({\bf R}\…

Adic Foxby Classes

We continue our work on adic semidualizing complexes over a commutative noetherian ring $R$ by investigating the associated Auslander and Bass classes (collectively known as Foxby classes), following Foxby and Christensen. Fundamental properties of these classes include Foxby Equivalence, which provides an equivalence between the Auslander and Bass classes associated to a given adic semidualizing complex. We prove a variety of stability results for these classes, for instance, with respect to $F\otimes^{\mathbf{L}}_R-$ where $F$ is an $R$-complex finite flat dimension, including special conver…

秩为2的自由结合代数的自守等价问题

Automorphic equivalence problem for free associative algebras of rank two

设K <x，y>是任意特征的代数闭构造域上秩为2的自由结合代数.本文给出了一个判定K <x，y>中的两个元素在K <x，y>的自同构下是否等价的算法。我们的算法的一个修改解决的问题是否K <x，y>中的元素是一个非平凡的自同构的半不变。特别地，它确定元素是否在Aut K <x，y>中具有非平凡稳定子。Wightwick给出了C [x，y]中多项式在自同构下等价的一个算法。另一个简单得多的算法，对于任何代数闭的构造域K，K [x，y]中两个多项式的自守等价由Makar-Limanov，Shpilrain和Yu给出。在我们的方法中，我们结合了后三位作者的想法与来自未发表论文的莱恩用来描述稳定K <x，y>元素的自同构的想法。这也允许我们给出由Makar-Limanov，Shpilrain和Yu得到的K [x，y]的相应结果的简单证明。

相对 Cohen-Macaulay 模范畴的对偶与等价

Dualities and equivalences of the category of relative Cohen-Macaulay modules

本文发展相对 Cohen-Macaulay 模理论，引入 a-相对对偶化模与大 Cohen-Macaulay 模，建立局部代数对偶的整体版本，并考察其在 Foxby 等价下的范畴行为。