MOD-RETRACTABLE RINGS

Kosan M. T., Zemlicka J.

COMMUNICATIONS IN ALGEBRA, cilt.42, sa.3, ss.998-1010, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1080/00927872.2012.721430
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.998-1010
  • Anahtar Kelimeler: Group module, Max rings, Noetherian rings, Nonsingular rings, Perfect rings, Retractable module, Semiartinian rings, 16D50, ENDOMORPHISM-RINGS, COMMUTATIVE RINGS, BAER MODULES, DIRECT SUMS, SUBMODULES
  • Gazi Üniversitesi Adresli: Hayır

Özet

A right module M over a ring R is said to be retractable if Hom(R)(M, N)0 for each nonzero submodule N of M. We show that M circle times(R)RG is a retractable RG-module if and only if M-R is retractable for every finite group G. The ring R is (finitely) mod-retractable if every (finitely generated) right R-module is retractable. Some comparisons between max rings, semiartinian rings, perfect rings, noetherian rings, nonsingular rings, and mod-retractable rings are investigated. In particular, we prove ring-theoretical criteria of right mod-retractability for classes of all commutative, left perfect, and right noetherian rings.