Theorems · Theorem · commutative algebra
TensorProduct.spanFinrank_top_eq_of_residueField
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_3} [inst_1 : AddCommGroup M] [inst_2 : Module R M] (N : Submodule R M)
[inst_3 : IsLocalRing R], N.FG → ⊤.spanFinrank = N.spanFinrank- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Set.imageproof · cited by 5,609
- Cardinalproof · cited by 2,598
- TensorProductstatement and proof · cited by 2,545
- le_reflproof · cited by 2,061
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.spanFinrank_eq_finrank_quotientproof · cited by 1