Cohereditary modules in sigma[M]


KESKİN TÜTÜNCÜ D., Ertas N. O. , Tribak R.

International Conference on Modules and Comodules, Porto, Portekiz, 6 - 08 Eylül 2006, ss.265-268 identifier

  • Cilt numarası:
  • Doi Numarası: 10.1007/978-3-7643-8742-6_17
  • Basıldığı Şehir: Porto
  • Basıldığı Ülke: Portekiz
  • Sayfa Sayıları: ss.265-268

Özet

A module N is an element of sigma[M] is called cohereditary in sigma[M] if every factor module of N is injective in sigma[M]. This paper explores the properties and the structure of some classes of cohereditary modules. Among others, we prove that any cohereditary lifting semi-artinian module in a[M] is a direct sum of Artinian uniserial modules. We show that over a commutative ring a lifting module N with small radical is cohereditary in a[M] if and only if N is semisimple M-injective. It is also shown that if E is an indecomposable injective module over a commutative Noetherian ring R with associated prime ideal p, then E is cohereditary lifting if and only if there is only one maximal ideal m over p and the ring R-m is a discrete valuation ring.