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I would like to have some geometric intuition for - Noetherian rings/modules - Local rings - Projective modules - Injective modules

As an illustration of what I am looking for, I was told once that that for a local ring to be a domain roughly means that locally a curve has only one component.

Thanks

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    ... component passing through it. In this sense, geometry gives you intuition for Noetherian rings. Algebraic vector bundles on varieties correspond to locally free coherent sheaves - over affine varieties, these are locally free Noetherian modules.2012-12-07

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