Cohereditary modules in sigma[M]

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

International Conference on Modules and Comodules, Porto, Portugal, 6 - 08 September 2006, pp.265-268, (Full Text)

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • Doi Number: 10.1007/978-3-7643-8742-6_17
  • City: Porto
  • Country: Portugal
  • Page Numbers: pp.265-268
  • Süleyman Demirel University Affiliated: Yes

Abstract

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.