- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Modules satisfying certain chain conditions and their endomorphisms Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 549-556 https://doi.org/10.4134/BKMS.2015.52.2.549Published online March 31, 2015 Fanggui Wang and Hwankoo Kim Sichuan Normal University, Hoseo University Abstract : In this paper, we characterize $w$-Noetherian modules in terms of polynomial modules and $w$-Nagata modules. Then it is shown that for a finite type $w$-module $M$, every $w$-epimorphism of $M$ onto itself is an isomorphism. We also define and study the concepts of $w$-Artinian modules and $w$-simple modules. By using these concepts, it is shown that for a $w$-Artinian module $M$, every $w$-monomorphism of $M$ onto itself is an isomorphism and that for a $w$-simple module $M$, $\End_R M$ is a division ring. Keywords : GV-torsion-free, $w$-module, $w$-Noetherian module, $w$-simple module, $w$-Artinian module MSC numbers : 13A15, 13E05, 13E10 Downloads: Full-text PDF