项目名称: 相对同调理论与导出范畴
项目编号: No.11201376
项目类型: 青年科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 张文汇
作者单位: 西北师范大学
项目金额: 23万元
中文摘要: 本项目旨在通过对相对同调理论的研究,寻求模范畴和模复形范畴中更多的同调性质和不变量。经典同调代数和相对同调代数是在模范畴中利用传统的同调方法展开的。本项目将利用更为有效的工具- - 导出范畴方法和倾斜理论,来发现新的覆盖类和包络类,通过对模及复形的各种覆盖、包络存在性和完备性的考查,研究广义导出函子, 得到计算同调维数的新途径;借助对模与复形的相对同调性质和不变量的研究,来得到一些重要环类的结构和性质。同时,研究相对同调理论在倾斜理论和导出范畴中的应用。本项目将导出范畴方法应用于模与复形相对同调理论的研究,对于进一步丰富和发展相对同调代数具有重要意义。
中文关键词: 覆盖;包络;C-E复形;几乎可裂序列;
英文摘要: The purpose of the project is to quest for new homological properties and invariants of modules and complexes of modules, by way of the research of relative homological theories. Traditional homological methods are always adopted to develop homological algebra regardless of classical or relative . In the study, we will find some new (pre)covering class and (pre)enveloping class, adopting more effective derived category methods and tilting theories. By means of investigating the existence and completeness of all kinds of covers and envelopes by cotorsion theory, then to investigate various generalized Ext and Tor functions, to abtain new approach for computing homological dimensions. And that can study the properties and structures of some important ring class. At the same time, We discuss the application of relative homological theories in tilting theories and derived categories. Derived category methods are applied in the project, which have very impotant significance for further enriching and developing relative homological algebra.
英文关键词: cover;envelope;C-E complexes;almost split sequences;