MODULES THAT HAVE A WEAK SUPPLEMENT IN EVERY EXTENSION
MISKOLC MATHEMATICAL NOTES, cilt.17, sa.1, ss.471-481, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 17 Sayı: 1
- Basım Tarihi: 2016
- Doi Numarası: 10.18514/mmn.2016.1424
- Dergi Adı: MISKOLC MATHEMATICAL NOTES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.471-481
- Anahtar Kelimeler: weak supplement, coatomic extension, semilocal ring, left perfect ring
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
We say that over an arbitrary ring a module M has the property. (WE) (respectively, (WEE)) if M has a weak supplement (respectively, ample weak supplements) in every extension. In this paper, we provide various properties of modules with these properties. We show that a module M has the property. (WEE) iff every submodule of M has the property. (WE). A ring R is left perfect iff every left R-module has the property. (WE) iff every left R-module has the property. (WEE). A ring R is semilocal iff every left R-module has a weak supplement in every extension with small radical. We also study modules that have a weak supplement(respectively, ample weak supplements) in every coatomic extension, namely the property. (WE*) (respectively,. (WEE*)).