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.
(c) A has a composition series.
(d) A satisfies both the ascending and descending chain conditions on submodules
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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...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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