Theorems · Theorem · commutative algebra

Ideal.map_mk_comap_factorPow

∀ {R : Type u_3} [inst : CommRing R] (I : Ideal R) {a b : ℕ},
  0 < a →
    ∀ (le : a ≤ b),
      Ideal.comap (Ideal.Quotient.factorPow I le) (Ideal.map (Ideal.Quotient.mk (I ^ a)) I) =
        Ideal.map (Ideal.Quotient.mk (I ^ b)) I

Defined in: Mathlib.RingTheory.Ideal.Quotient.PowTransition
Cited by: 0 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
RingHomstatement · cited by 10,189
Idealstatement and proof · cited by 4,748
HasQuotient.Quotientstatement · cited by 2,301
Ideal.mapstatement · cited by 692
Ideal.Quotient.mkstatement · cited by 610
Ideal.comapstatement · cited by 443
Ideal.Quotient.factorPowstatement · cited by 18
Ideal.pow_le_selfproof · cited by 16
Ideal.map_mk_comap_factorproof · cited by 1

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