Theorems · Theorem · commutative algebra
mem_integralClosure_iff_mem_fg
∀ (R : Type u_1) (A : Type u_2) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {r : A},
r ∈ integralClosure R A ↔ ∃ M, (Subalgebra.toSubmodule M).FG ∧ r ∈ M- Cited by
- 1 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Submodulestatement · cited by 7,192
- Subalgebrastatement and proof · cited by 1,353
- OrderEmbeddingstatement · cited by 619
- Algebra.adjoinproof · cited by 535
- Submodule.FGstatement and proof · cited by 230
- Subalgebra.toSubmodulestatement and proof · cited by 141
- Algebra.subset_adjoinproof · cited by 109
- integralClosurestatement and proof · cited by 105
- IsIntegral.fg_adjoin_singletonproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.coe_ideal_mul_invproof · cited by 1