Injectivity relative to closed submodules

MERMUT E., Santa-Clara C., Smith P. F.

JOURNAL OF ALGEBRA, cilt.321, sa.2, ss.548-557, 2009 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 321 Sayı: 2
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1016/j.jalgebra.2008.11.004
  • Dergi Adı: JOURNAL OF ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.548-557
  • Anahtar Kelimeler: Injective module, Closed submodule, Dedekind domain, Primitive ideal
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Let R be a ring. An R-module X is called c-injective if, for every closed submodule L of every R-module M, every homomorphism from L to X lifts to M. It is proved that if R is a Dedekind domain then an R-module X is c-injective if and only if X is isomorphic to a direct product of homogeneous semisimple R-modules and injective R-modules. It is also proved that a commutative Noetherian domain R is Dedekind if and only if every simple R-module is c-injective. (C) 2008 Elsevier Inc. All rights reserved.