Generalizations of von Neumann regular rings, PP rings, and Baer rings  

作　　者：Lixin MAO 

机构地区：[1]Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167,China

出　　处：《Frontiers of Mathematics in China》2016年第2期377-400,共24页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11171149, 11371187）, Jiangsu 333 Project, and Jiangsu Six Major Talents Peak Project.

摘　　要：We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer modules.We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer modules.

关 键 词：IDS Module IP module Baer＊ module von Neumann regularring PP ring Baer ring 

分 类 号：O153.3[理学—数学] TQ426.61[理学—基础数学]