Theorems · Theorem · commutative algebra
Algebra.finite_adjoin_simple_of_isIntegral
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] {x : B},
IsIntegral R x → Module.Finite R ↥R[x]- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Subalgebrastatement · cited by 1,353
- Module.Finitestatement · cited by 1,032
- Algebra.adjoinstatement · cited by 535
- IsIntegralstatement and proof · cited by 427
- Module.Finite.of_fgproof · cited by 21
- IsIntegral.fg_adjoin_singletonproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.QuasiFinite.of_isIntegral_of_finiteTypeproof · cited by 1