Theorems · Theorem · commutative algebra
Algebra.isIntegral_norm
∀ {R : Type u_1} [inst : CommRing R] {L : Type u_6} (K : Type u_7) [inst_1 : Field K] [inst_2 : Field L]
[inst_3 : Algebra K L] [inst_4 : Algebra R L] [inst_5 : Algebra R K] [IsScalarTower R K L] {x : L},
IsIntegral R x → IsIntegral R ((Algebra.norm K) x)- Defined in
- Mathlib.RingTheory.Norm.Transitivity
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
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
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- MonoidHomstatement · cited by 3,629
- FiniteDimensionalproof · cited by 1,854
- MulZeroClass.zero_mulproof · cited by 1,625
- Fintype.cardproof · cited by 1,386
- IntermediateFieldproof · cited by 988
Cited by4
Results whose statement or proof uses this declaration.
- dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- prod_galRestrict_eq_normstatement and proof · cited by 1
- mem_adjoin_of_smul_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- Algebra.algebraMap_intNorm_of_isGaloisproof · cited by 1