Theorems · Theorem · commutative algebra
IsIntegral.algebraMap
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Ring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : Algebra A B] [IsScalarTower R A B] {x : A},
IsIntegral R x → IsIntegral R ((algebraMap A B) x)- Cited by
- 15 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- map_zeroproof · cited by 1,614
- Polynomial.Monicproof · cited by 461
- IsIntegralstatement and proof · cited by 427
- Polynomial.eval₂proof · cited by 267
Cited by15
Results whose statement or proof uses this declaration.
- IsGaloisGroup.of_isFractionRingproof · cited by 5
- IsLocalization.integralClosureproof · cited by 3
- IsIntegralClosure.algebraMap_liftproof · cited by 3
- IsIntegralClosure.range_le_span_dualBasisproof · cited by 2
- IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_powproof · cited by 1
- Algebra.algebraMap_intNorm_of_isGaloisproof · cited by 1
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1
- Algebra.QuasiFinite.of_isIntegral_of_finiteTypeproof · cited by 1
- prod_galRestrict_eq_normstatement and proof · cited by 1
- IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosureproof · cited by 0
- Algebra.ZariskisMainProperty.transproof · cited by 0