Theorems · Theorem · commutative algebra

AdjoinRoot.quotEquivQuotMap_apply

∀ {R : Type u_1} [inst : CommRing R] (f : Polynomial R) (I : Ideal R)
  (a : AdjoinRoot f ⧸ Ideal.map (AdjoinRoot.of f) I),
  (AdjoinRoot.quotEquivQuotMap f I) a = (AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot I f) a

Defined in: Mathlib.RingTheory.AdjoinRoot
Cited by: 1 results in Mathlib
Foundations: Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Cites17

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
Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
RingHomstatement · cited by 10,189
Polynomialstatement and proof · cited by 5,681
Idealstatement and proof · cited by 4,748
HasQuotient.Quotientstatement and proof · cited by 2,301
AlgEquivstatement · cited by 1,681
RingEquivstatement · cited by 1,147
Ideal.spanstatement · cited by 948
Polynomial.mapstatement · cited by 806
Ideal.mapstatement and proof · cited by 692

Cited by1

Results whose statement or proof uses this declaration.

AdjoinRoot.quotEquivQuotMap_apply_mkproof · cited by 1