Question

If direct sum of every injective module is injective then the ring will be noetherian

Answer 1

Answer:

Yeah,

If direct sum of every injective module is injective then the ring will be noetherian,

so each injective ME q, is a direct sum of indecomposable injective modules. If M is in- decomposable injective, then M is the injective hull of any nonzero submodule.

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Answer 2

Answer -

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• The Bass-Papp Theorem asserts that a commutative ring R is Noetherian iff every direct sum of injective R-modules is injective. Thus every non-Noetherian.

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