On Baer–Kaplansky Classes of Modules-Reference-Cited by-同舟云学术

On Baer–Kaplansky Classes of Modules

Published:2017-11-15 Issue:04 Volume:24 Page:603-610
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Tütüncü Derya Keskin¹,Tribak Rachid²

Affiliation:

1. Department of Mathematics, Hacettepe University, 06800 Beytepe, Ankara, Turkey

2. Centre Régional des Métiers de L’Education et de la Formation (CRMEF)-Tanger, Avenue My Abdelaziz, Souani, B.P. 3117, Tangier, Morocco

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386717000396

Reference7 articles.

1. A class of balanced non-uniserial rings

2. Quasi-projective abelian groups

3. Structure of some noetherian SI rings

4. Generalizing the Baer-Kaplansky Theorem

5. A Characterization of FGC Rings

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An investigation of the Baer–Kaplansky property;São Paulo Journal of Mathematical Sciences;2024-02-27

2. Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants;Communications in Algebra;2022-09-30

3. Baer-Kaplansky Theorem for Modules over Non-commutative Algebras;KYUNGPOOK MATH J;2021

4. Baer-Kaplansky classes in categories: transfer via functors;Communications in Algebra;2020-02-25

5. Baer–Kaplansky Classes in Grothendieck Categories and Applications;Mediterranean Journal of Mathematics;2019-06-20