A variation of supplemented modules
TURKISH JOURNAL OF MATHEMATICS, cilt.37, sa.3, ss.418-426, 2013 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 37 Sayı: 3
- Basım Tarihi: 2013
- Doi Numarası: 10.3906/mat-1108-20
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.418-426
- Anahtar Kelimeler: Modules, omega-supplemented, Dedekind domain
- Dokuz Eylül Üniversitesi Adresli: Evet
Özet
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.