Speaker: 扶先辉教授，东北师范大学

Inviter: 陈亦飞副研究员

Title: Ghosts, phantoms and Cartan-Eilenberg homological algebra for a DG-ring

Language: Chinese

Time & Venue: 2024.11.29 09:00-10:00 思源楼 S817

Abstract: We firstly investigate the ghost ideal and the phantom ideal in the (derived) category of DG-modules of a DG-ring. This allows us to introduce and investigate the notions of a Cartan-Eilenberg projective module, a Cartan-Eilenberg injective module, and a Cartan-Eilenberg flat module for a DG-ring. An immediate application is that we can give an affirmative answer to a conjecture of Minamoto. Also we may investigate Notherian DG-ring from our approach, and parallel to classical theory of rings and modules, introduce and investigate the notions of a coherent DG-ring, and a perfect DG-ring. We also investigate the global dimension and weakly global dimension of a DG-ring in the sense of Hovey and Lockridge. This talk is based on an ongoing project with Wei Hu amd Xiaoyan Yang.