Theorems · Theorem · commutative algebra

minpoly.ToAdjoin.injective

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [IsDomain R] [inst_3 : Algebra R S]
  [IsIntegrallyClosed R] [IsDomain S] [Module.IsTorsionFree R S] {x : S},
  IsIntegral R x → Function.Injective ⇑(AdjoinRoot.Minpoly.toAdjoin R x)

Defined in: Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed
Cited by: 0 results in Mathlib
Foundations: Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing IsDomain Algebra IsIntegrallyClosed IsDomain Module.IsTorsionFree

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DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Polynomialproof · cited by 5,681
AlgHomstatement · cited by 3,236
IsDomainstatement and proof · cited by 2,196
Subalgebrastatement · cited by 1,353
Module.IsTorsionFreestatement and proof · cited by 600
Algebra.adjoinstatement and proof · cited by 535
minpolystatement and proof · cited by 439
IsIntegralstatement and proof · cited by 427

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