Theorems · Theorem · commutative algebra
IsIntegrallyClosed.algebraMap_eq_of_integral
∀ {R : Type u_1} [inst : CommRing R] {K : Type u_3} [inst_1 : CommRing K] [inst_2 : Algebra R K]
[ifr : IsFractionRing R K] [IsIntegrallyClosed R] {x : K}, IsIntegral R x → ∃ y, (algebraMap R K) y = x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- IsFractionRingstatement and proof · cited by 738
- IsIntegralstatement · cited by 427
- IsIntegrallyClosedstatement and proof · cited by 203
- IsIntegralClosure.isIntegral_iffproof · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- IsIntegrallyClosed.pow_dvd_pow_iffproof · cited by 2
- IsIntegral.exists_int_iff_exists_ratproof · cited by 1
- maximalIdeal_isPrincipal_of_isDedekindDomainproof · cited by 1
- Algebra.isInvariant_of_isGaloisproof · cited by 0