Modules with Unique Closure Relative to a Torsion Theory. III

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Dogruoz S., Harmanci A., Smith P. F.

UKRAINIAN MATHEMATICAL JOURNAL, cilt.66, sa.7, ss.1028-1036, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 66 Sayı: 7
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s11253-014-0992-x
  • Dergi Adı: UKRAINIAN MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1028-1036
  • Hacettepe Üniversitesi Adresli: Evet

Özet

We continue the study of modules over a general ring R whose submodules have a unique closure relative to a hereditary torsion theory on Mod-R. It is proved that, for a given ring R and a hereditary torsion theory tau on Mod-R, every submodule of every right R-module has a unique closure with respect to tau if and only if tau is generated by projective simple right R-modules. In particular, a ring R is a right Kasch ring if and only if every submodule of every right R-module has a unique closure with respect to the Lambek torsion theory.