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Rings with nice Artinian Modules

Aziz El Mejdani, H. Essannouni, A. Kaidi

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Abstract

Over a Dedekind domain D, every artinian D-module M is a direct sum of a module of finite length and of a finite number of injective hulls of simple modules, M = F ⊕ ( n i=1 E(S i)). In this paper we give more general examples of classes of rings over which the artinian modules have the same decomposition and we characterize commutative co-noetherian rings having this property.

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What this paper is about

Over a Dedekind domain D, every artinian D-module M is a direct sum of a module of finite length and of a finite number of injective hulls of simple modules, M = F ⊕ ( n i=1 E(S i)). In this paper we give more general examples of classes of rings over which the artinian modules have the same decomposition and we characterize commutative co-noetherian rings having this property.

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Available abstract

Over a Dedekind domain D, every artinian D-module M is a direct sum of a module of finite length and of a finite number of injective hulls of simple modules, M = F ⊕ ( n i=1 E(S i)). In this paper we give more general examples of classes of rings over which the artinian modules have the same decomposition and we characterize commutative co-noetherian rings having this property.

Key concepts: Mathematics, Semisimple module, Artinian ring, Injective module, Pure mathematics, Noncommutative ring, Noetherian, Simple module

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