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.
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This paper is dedicated to Professor Robert Wisbauer on his 65th birthday
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Tütüncü, D.K., Ertaş, N.O., Tribak, R. (2008). Cohereditary Modules in σ[M]. In: Brzeziński, T., Gómez Pardo, J.L., Shestakov, I., Smith, P.F. (eds) Modules and Comodules. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8742-6_17
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DOI: https://doi.org/10.1007/978-3-7643-8742-6_17
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