Cotorsion pairs induced by duality pairs

Duality pairs, generalized Gorenstein modules, and Ding injective envelopes

Let $R$ be a general ring. Duality pairs of $R$-modules were introduced by Holm-Jorgensen. Most examples satisfy further properties making them what we call semi-complete duality pairs in this paper. We attach a relative theory of Gorenstein homological algebra to any given semi-complete duality pair $\mathfrak{D} = (\mathcal{L},\mathcal{A})$. This generalizes the homological theory of the AC-Gorenstein modules defined by Bravo-Gillespie-Hovey, and we apply this to other semi-complete duality pairs. The main application is that the Ding injective modules are the right side of a complete (perfe…

交换诺特环上的余挠对与 Tor-对

Cotorsion pairs and Tor-pairs over commutative noetherian rings

本文对交换诺特环上的遗传余挠对进行分类，利用环谱上的整值函数和局部深度条件描述左类，并通过对偶对应到遗传 Tor-对。

关于遗传挠理论的余挠模

Cotorsion modules relative to a hereditary torsion theory

本文针对遗传挠理论τ_w，引入Tor对、余挠对及强平坦模，以此刻画完全环等多种已知环类。

由平衡对诱导的Gorenstein余挠对

Gorenstein cotorsion pairs induced by balanced pairs

本文研究局部可表示阿贝尔范畴中由容许平衡对诱导的恰当结构，证明相关Gorenstein类构成遗传余挠对，并给出相对纯性下的函子完备性判据及Dedekind域上的显式计算。

Lex 理想的 Hilbert 函数与商之间的对偶性

A Duality between Hilbert Functions of Lex Ideals and Quotients

本文研究单项式理想与商诱导的 Macaulay 系数，给出显式公式并证明两者构成集合划分的对偶性。

相对于对偶对的 Gorenstein 平坦模与复形的同调和同伦方面

Homological and homotopical aspects of Gorenstein flat modules and complexes relative to duality pairs

本文研究相对于对偶对的 Gorenstein 平坦模与复形，证明其封闭性、维数性质及 Pontryagin 对偶，并构造相关 Abel 模型结构与同伦范畴 recollement。