单边 Gorenstein 复形
One-Sided Gorenstein Complexes
DOI: 10.12677/PM.2021.1112223, PDF, HTML, 下载: 352  浏览: 1,423  国家自然科学基金支持
作者: 李彦洁：西北师范大学数学与统计学院，甘肃 兰州
关键词: 自正交类；右 (左) W-Gorenstein 模；右 (左) W-Gorenstein 复形；Self-Orthogonal Class； Right (Left) W-Gorenstein Modules； Right (Left) W-Gorenstein Complexes
摘要: 设 W 是一个关于扩张封闭的自正交左 R-模类。 引入了右 (左) W-Gorenstein 复形的概念，证明了复形 M 是右 (左) W-Gorenstein复形当且仅当对任意的 n ∈ℤ， Mn 是右 (左) W-Gorenstein 模。 作为应用，由右 (左) W-Gorenstein 模的性质推得了右 (左) W-Gorenstein复形的一些性质。
Abstract: Let W be a self-orthogonal class of left R-modules which is closed under extensions. In this article, the notion of right (left) W-Gorenstein complexes is introduced, and we show that a complex M is right (left) W-Gorenstein if and only if each Mn is right (left) W-Gorenstein module for any n ∈ Z. As applications, some properties of right (left) W-Gorenstein complexes are deduced from those of right (left) W-Gorenstein modules.
文章引用：李彦洁. 单边 Gorenstein 复形[J]. 理论数学, 2021, 11(12): 2003-2011. https://doi.org/10.12677/PM.2021.1112223

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