On Finitely Generated Projective Modules and Exchange Rings

• 来源期刊: 代数集刊（英文版）
• 关键词: exchange ring nth root projective module
• 年，卷（期）: 2002,（4）
• 页码范围: 433-444
• 页数: 12页
• 语种: 英文

摘要

In this paper, we study the relation between exchange rings R and their J-semisimple indecomposable factor rings. In particular, we prove that for any exchange ring R and any finitely generated projective R-modules P and Q,P is isomorphic to a direct summand of Q if and only if for every ideal I of R such that R/I is indecomposable and J-semisimple, the right R/I-module P/PI is isomorphic to a direct summand of Q/QI.