Modules that have a supplement in every cofinite extension

Çalışıcı H., TÜRKMEN E.

GEORGIAN MATHEMATICAL JOURNAL, cilt.19, sa.2, ss.209-216, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 2
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1515/gmj-2012-0018
  • Dergi Adı: GEORGIAN MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.209-216
  • Anahtar Kelimeler: Supplement, cofinite extension, semiperfect ring
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

Let R be a ring and M a left R-module. An R-module N is called a cofinite extension of M in case M subset of N and N/M is finitely generated. We say that M has the property (CE) (resp. (CEE)) if M has a supplement (resp. ample supplements) in every cofinite extension. In this study we give various properties of modules with these properties. We show that a module M has the property (CEE) iff every submodule of M has the property (CE). A ring R is semiperfect iff every left R-module has the property (CE). We also study cofinitely injective modules, direct summands of every cofinite extension, as a generalization of injective modules.