Name: Idempotent and Nilpotent Submodules of Multiplication Modules
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Author: Ali, Majid ; Smith, David
ISBN: 9783330041189

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portada Idempotent and Nilpotent Submodules of Multiplication Modules

Idempotent and Nilpotent Submodules of Multiplication Modules

Type

Physical Book

Author

David Smith

Majid Ali

Publisher

LAP Lambert Academic Publishing

Language

English

Pages

144

Format

Paperback

Dimensions

22.9 x 15.2 x 0.9 cm

Weight

0.22 kg.

ISBN13

9783330041189

Synopsis "Idempotent and Nilpotent Submodules of Multiplication Modules"

All rings are commutative with identity, and all modules are unital. The purpose of this article is to investigate multiplication von Neumann regular modules. For this reason we introduce the concept of nilpotent submodules generalizing nilpotent ideals and then prove that a faithful multiplication module is von Neumann regular if and only if it has no nonzero nilpotent elements and its Krull dimension is zero. We also give a new characterization for the radical of a submodule of a multiplication module and show in particular that the radical of any submodule of a Noetherian multiplication module is a finite intersection of prime submodules.

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Idempotent and Nilpotent Submodules of Multiplication Modules - Ali, Majid ; Smith, David

Synopsis "Idempotent and Nilpotent Submodules of Multiplication Modules"

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