Theorems · Theorem · commutative algebra
Algebra.IsIntegral.tower_top
∀ (R : Type u_1) {S : Type u_4} {T : Type u_5} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T]
[h : Algebra.IsIntegral R T], Algebra.IsIntegral S TLet T / S / R be a tower of algebras, T is an integral R-algebra, then it is integral
as an S-algebra.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Algebra.IsIntegralstatement and proof · cited by 224
- IsScalarTower.algebraMap_eqproof · cited by 110
- Algebra.IsIntegral.isIntegralproof · cited by 86
- RingHom.IsIntegralproof · cited by 54
- RingHom.IsIntegral.tower_topproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.normalizedTrace_trans_applyproof · cited by 1
- NumberField.maximalRealSubfield_eq_top_iff_isTotallyRealproof · cited by 0
- Ideal.ncard_primesOver_mul_ncard_primesOverproof · cited by 0