The following conditions on a semi simple module A are equivalent (a) A is finitely generated (b) A is a direct sum of a finite number of simple submodules (c) A has a composition series (d) A satisfies both the ascending and descending chain conditions on submodules ...

These conditions are all equivalent for a semisimple module A Lets prove the equivalence of these statements First lets clarify some definitions Semisimple Module A module is called semisimple if it i ...

The following conditions on a semi simple module A are equivalent: (a) A is finitely generated. (b)

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The following conditions on a semi simple module A are equivalent:

(a) A is finitely generated.

(b) A is a direct sum of a finite number of simple submodules.

(d) A satisfies both the ascending and descending chain conditions on submodules

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Aug 03, 2023 08:22 AM

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The following conditions on a semi simple module A are equivalent: (a) A is finitely generated. (b)

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Algebra Graduate Texts In Mathematics 73

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