← Theoretical / proof-based

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In this program

Noetherian and Artinian rings and modules
Primary decomposition in Noetherian rings
Integral extensions
Going-up/going-down theorems
Dedekind domains and DVRs
Tensor products
Flatness (introduction)

Rings and modules

Going-up/going-down theorems

Commutative algebra · Theoretical / proof-based

Topic

Going-up/going-down theorems

Practice by unit: Rings and modules

Graduate Commutative Algebra — scope drawn from open commutative algebra notes and typical US graduate commutative algebra syllabi.

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