On Baer-Kaplansky Classes of Modules  

作　　者：Derya Keskin Tutuncu Rachid Tribak 

机构地区：[1]Department of Mathematics, Hacettepe University 06800 Beytepe, Ankara, Turkey [2]Centre Regional des Metiers de L'Education et de la Formation (CRMEF)-Tanger Avenue My Abdelaziz, Souani, B.P. 3117, Thngier, Morocco

出　　处：《Algebra Colloquium》2017年第4期603-610,共8页代数集刊（英文版）

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.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.

关 键 词：Baer Kaplansky class of modules local modules semisimple rings 

分 类 号：O1[理学—数学]