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Cohereditary Modules in σ[M]

  • Derya Keskin Tütüncü
  • Nil Orhan Ertaş
  • Rachid Tribak
Part of the Trends in Mathematics book series (TM)

Abstract

A module N ∈ σ[M] is called cohereditary in σ[M] if every factor module of N is injective in σ[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 σ[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 σ[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.

Keywords

Cohereditary module Lifting module Injective module Semisimple module 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Derya Keskin Tütüncü
    • 1
  • Nil Orhan Ertaş
    • 2
  • Rachid Tribak
    • 3
  1. 1.Department of MathematicsHacettepe UniversityBeytepe AnkaraTurkey
  2. 2.Department of MathematicsSüleyman Demirel UniversityCünür IspartaTurkey
  3. 3.Département de mathématiquesFaculté des sciences de TétouanTétouanMorocco

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