报告题目：Ghosts, phantoms, and Cartan-Eilenberg homological algebra for a DG-ring
报告人：杨晓燕教授，浙江科技大学
报告时间：2024年11月26日（周二）14:00-15:00
报告地点：20-200
报告摘要：We firstly investigate the ghost ideal and the phantom ideal, respectively, in the derived category of a DG-ring. This allow us to introduce and investigate the notions of Cartan-Eilenberg projective modules, Cartan-Eilenberg injective modules, and Cartan-Eilenberg flat modules. By this way, we develope a theory of Cartan-Eilenberg homological algebra for a DG-ring. An immediate application of the above theory is that we give an affirmative answer to a conjecture of Minamoto. As another direction of the application of this theory, we may investiage Notherian DG-ring from this approach, and parellal to classical ring theory, introduce and investigate the notions of a hereditary DG-ring, a coherent DG-ring, and a perfect DG-ring. This work joint with Xianhui Fu and Wei Hu.
报告人简介：杨晓燕，浙江科技大学理学院教授、博士生导师，主要从事环的同调理论、导出范畴等领域的研究。已在J.Algebra、Forum Math.等国际顶尖期刊发表SCI论文50余篇。入选教育部新世纪优秀人才支持计划、甘肃省飞天学者特聘计划青年学者项目，主持完成国家自然科学项目3项；现为美国《Math Review》评论员，中国高等教育学会教育数学专业委员会理事；负责建设的《高等代数》获批甘肃省线上线下混合式一流课程。
邀请人：魏加群