Let R be a ring that (as a left R module) is the sum of its minimal left ideals Assume that r R I Rr 0 0 If A is an R module such that RA A, then A is semi simple ...

To prove that the Rmodule A is semisimple we need to show that A is a direct sum of simple submodules Recall that a submodule ...

Let R be a ring that (as a left R-module) is the sum of its minimal left

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Let R be a ring that (as a left R-module) is the sum of its minimal left ideals. Assume that {r ϵ R I Rr = 0} = 0. If A is an R-module such that RA = A, then A is semi simple.

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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 08:20 AM

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Let R be a ring that (as a left R-module) is the sum of its minimal left

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To prove that the Rmodule A is semisimple we need to show that A is a direct sum of simple submodules Recall that a submodule ...View the full answer

Algebra Graduate Texts In Mathematics 73

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