A variation of supplemented modules
TURKISH JOURNAL OF MATHEMATICS, vol.37, no.3, pp.418-426, 2013 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 37 Issue: 3
- Publication Date: 2013
- Doi Number: 10.3906/mat-1108-20
- Journal Name: TURKISH JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.418-426
- Keywords: Modules, omega-supplemented, Dedekind domain
- Dokuz Eylül University Affiliated: Yes
Abstract
Over a general ring, an R-module is omega-supplemented if and only if amply omega-supplemented. It is proved that over a local Dedekind domain, all modules are omega-supplemented and over a non-local Dedekind domain, an R-module M is omega-supplemented if and only if Soc(M) << M or M = S-0 circle plus (circle plus(i is an element of I) K), where S-0 is a torsion, semisimple submodule of M and K is the field of quotients of R.