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Idempotent ring elements #2009

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Alizter opened this issue Jul 1, 2024 · 0 comments
Open

Idempotent ring elements #2009

Alizter opened this issue Jul 1, 2024 · 0 comments
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@Alizter
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Alizter commented Jul 1, 2024

We should define what it means for a ring element to be idempotent and prove some basic properties about them.

We should also link this to decomposition of $R$-modules. if $e$ is an idempotent element of $R$ then an $R$-module $M$ can be decomposed as $M \cong eM \oplus (1-e)M$. This will be important for an eventual proof of the Wedderburn-Artin theorem.

@Alizter Alizter added the algebra label Jul 2, 2024
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