强余纯模的性质及其应用

发布时间：2018-04-04 11:11

本文选题：强余纯投射模　切入点：强余纯内射模　出处：《南京大学》2015年博士论文

【摘要】：在相对同调代数中,Gorenstein模及相关模类是重要的研究对象,这些模已经被很多作者研究过[6,9,10,14-19,21,28,31]。例如,Enochs和Jenda[14]引入了强余纯内射模和强余纯平坦模。Fu, Zhu和Ding [21]引入了强余纯投射模。容易看出每个Gorenstein内射模是强余纯内射模,并且每个Gorenstein平坦模是强余纯平坦模。由[17,Lemma 10.2.4],对左凝聚环R,每个有限表现Gorenstein投射左R-模是强余纯投射模。本文主要研究强余纯模。全文一共分为四章。第一章给出了研究背景和主要结果。第二章研究了强余纯模和对偶化模。假设R是右诺特环,S是左诺特环,并且存在一个对偶化S-R-双模,我们研究了强余纯内射左S-模,Gorenstein内射左S-模和Bass类召(S)中模之间的关系,以及强余纯投射(平坦)左R-模,Gorenstein投射(平坦)左R-模和Auslander类A(R)中模之间的关系。进而,我们给出了强余纯内射左S-模,强余纯投射左R-模及强余纯平坦左R-模的一些等价刻画。第三章研究了什么时候每个模有强余纯内射预盖,每个有限表现模有强余纯平坦预包和强余纯投射预包。进而,我们研究了相对导出函子和维数。第四章研究了强余纯模的同伦范畴。我们考虑了什么时候强余纯投射模的同伦范畴是紧生成的,并且给出了同伦范畴里的一些伴随函子和recollements。
[Abstract]:Gorenstein modules and related modules are important research objects in relative homology algebras. These modules have been studied by many authors.For example, Enochs and Jenda [14] introduce strong copure injective modules and strongly copure flat modules. Fu. Zhu and Ding [21] introduce strong copure projective modules.It is easy to see that every Gorenstein injective module is a strongly copure injective module, and every Gorenstein flat module is a strongly copure flat module.From [17] Lemma 10.2.4], for left coherent ring R, every finitely expressed Gorenstein projective left R-module is a strongly copure projective module.In this paper, we mainly study the strong purebred modules.The full text is divided into four chapters.The first chapter gives the research background and main results.In the second chapter, we study the strong copure modules and the dualized modules.Assuming that R is a right Nott ring S is a left Nott ring and there exists a dual S-R-Bimodule, we study the relation between the left S-module of strong copure injective left S-module and the left S-module of Bass class.And the relations between strongly copure projective (flat) left R -modules and Auslander class A (R) in the projective (flat) left R- module.Furthermore, we give some equivalent characterizations of strong copure injective left S-modules, strongly copure projective left R-modules and strongly copure flat left R-modules.In chapter 3, we study when every module has strong copure injective precover, every finite representation module has strong copure flat prepacket and strong copure projective prepacket.Furthermore, we study the relative derived functor and dimension.In chapter 4, we study the homotopy category of strong coputral modules.We consider when the homotopy categories of strongly copure projective modules are compactly generated and give some adjoint functors and recollementsin homotopy categories.
【学位授予单位】：南京大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O153.3

【共引文献】