On Baer-Kaplansky Classes of Modules

• 来源期刊: 代数集刊（英文版）
• 关键词: Baer-Kaplansky class of modules local modules semisimple rings
• 年，卷（期）: 2017,（4）
• 页码范围: 603-610
• 页数: 8页
• 语种: 英文
• DOI: 10.1142/S1005386717000396

摘要

We are interested in studying when the class of local modules is Baer-Kaplansky.We provide an example showing that even over a commutative semisimple ring R,we can find two non-isomorphic simple R-modules S1 and S2 such that the rings EndR(S1) and EndR(S2) are isomorphic.We show that over any ring R,the class of semisimple R-modules is Baer-Kaplansky if and only if so is the class of simple R-modules.