On some generalizations of closed submodules


Creative Commons License

Durgun Y.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, cilt.52, ss.1549-1557, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 52 Konu: 5
  • Basım Tarihi: 2015
  • Doi Numarası: 10.4134/bkms.2015.52.5.1549
  • Dergi Adı: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Sayfa Sayısı: ss.1549-1557

Özet

Characterizations of closed subgroups in abelian groups have been generalized to modules in essentially different ways; they are in general inequivalent. Here we consider the relations between these generalizations over commutative rings, and we characterize the commutative rings over which they coincide. These are exactly the commutative noetherian distributive rings. We also give a characterization of c-injective modules over commutative noetherian distributive rings. For a noetherian distributive ring R, we prove that, (1) direct product of simple R-modules is c-injective; (2) an R-module D is c-injective if and only if it is isomorphic to a direct summand of a direct product of simple R-modules and injective R-modules.