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Theorems · Theorem · algebraic geometry

PrimeSpectrum.zeroLocus_singleton_mul

∀ {R : Type u} [inst : CommSemiring R] (f g : R),
  PrimeSpectrum.zeroLocus {f * g} = PrimeSpectrum.zeroLocus {f} ∪ PrimeSpectrum.zeroLocus {g}
Defined in
Mathlib.RingTheory.Spectrum.Prime.Basic
Cited by
1 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
CommSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PrimeSpectrum.basicOpen_mul · cited by 5PrimeSpectrum.basicOpen_m…Set · cited by 53352SetCommSemiring · cited by 10911CommSemiringSet.ext · cited by 2266Set.extPrimeSpectrum · cited by 625PrimeSpectrumPrimeSpectrum.zeroLocus · cited by 164PrimeSpectrum.zeroLocusIdeal.IsPrime.mul_mem_iff_mem_or_mem · cited by 8IsPrime.mul_mem_iff_mem_o…PrimeSpectrum.zeroLocus_singl…CITED BYCITES

Cites6

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Cited by1

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