Theorems · Theorem · algebraic geometry

Module.rankAtStalk_prod

∀ {R : Type uR} (M : Type uM) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Flat R M]
  [Module.Finite R M] (N : Type u_1) [inst_5 : AddCommGroup N] [inst_6 : Module R N] [Module.Flat R N]
  [Module.Finite R N], Module.rankAtStalk (M × N) = Module.rankAtStalk M + Module.rankAtStalk N

The rank of M × N at p is equal to the sum of the ranks.

Defined in

Mathlib.RingTheory.Spectrum.Prime.FreeLocus

Cited by

2 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.FlatModule.FiniteAddCommGroupModuleModule.FlatModule.Finite