Theorems · Theorem · algebraic geometry

PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk

∀ {R : Type u_1} [inst : CommRing R] (c : R),
  (Set.range (PrimeSpectrum.comap (algebraMap (Polynomial R) (Polynomial (Localization.Away c)))))ᶜ =
    Set.range (PrimeSpectrum.comap (Polynomial.mapRingHom (Ideal.Quotient.mk (Ideal.span {c}))))

Defined in: Mathlib.RingTheory.Spectrum.Prime.Topology
Cited by: 0 results in Mathlib
Foundations: Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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DFunLike.coeproof · cited by 62,936
Setstatement and proof · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebraproof · cited by 11,388
SetLike.coeproof · cited by 8,199
Polynomialstatement and proof · cited by 5,681
Idealstatement · cited by 4,748
Algebra.algebraMapstatement and proof · cited by 4,706
Set.rangestatement and proof · cited by 4,705
Compl.complstatement and proof · cited by 2,925
HasQuotient.Quotientstatement and proof · cited by 2,301
Polynomial.Cproof · cited by 1,598

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