On essential extensions of direct sums of either injective or projective modules


Kosan M. T. , Truong Cong Quynh T. C. Q.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.13, sa.7, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Konu: 7
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1142/s0219498814500388
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Özet

For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum of injective right R-modules is injective, and R is right Noetherian if and only if every essential extension of a direct sum of injective hulls of simple right R-modules is a direct sum of injective right R-modules. In this paper, we prove that R is right Noetherian if and only if every essential extension of a direct sum of injective hulls of simple right R-modules is a direct sum of either injective right R-modules or projective right R-modules.