MODULES THAT HAVE A WEAK SUPPLEMENT IN EVERY EXTENSION

Onal E., Çalışıcı H., TÜRKMEN E.

MISKOLC MATHEMATICAL NOTES, cilt.17, sa.1, ss.471-481, 2016 (SCI-Expanded) identifier identifier

  • 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*)).