RAD-SUPPLEMENTING MODULES

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ÖZDEMİR S.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, cilt.53, sa.2, ss.403-414, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.4134/jkms.2016.53.2.403
  • Dergi Adı: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.403-414
  • Anahtar Kelimeler: supplement, Rad-supplement, supplementing module, Rad-supplementing module, perfect ring, RINGS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Let R be a ring, and let M be a left R-module. If M is Rad-supplementing, then every direct summand of M is Rad-supplementing, but not each factor module of M. Any finite direct sum of Rad-supplementing modules is Rad-supplementing. Every module with composition series is (Rad-)supplementing. M has a Rad-supplement in its injective envelope if and only if M has a Rad-supplement in every essential extension. R is left perfect if and only if R is semilocal, reduced and the free left R-module (R-R)((N)) is Rad-supplementing if and only if R is reduced and the free left R-module (R-R)((N)) is ample Rad-supplementing. M is ample Rad-supplementing if and only if every submodule of M is Rad-supplementing. Every left R-module is (ample) Rad-supplementing if and only if R/P(R) is left perfect, where P(R) is the sum of all left ideals I of R such that Rad I = I.