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Theorems · Theorem · algebraic geometry

PrimeSpectrum.union_zeroLocus

∀ {R : Type u} [inst : CommSemiring R] (s s' : Set R),
  PrimeSpectrum.zeroLocus s ∪ PrimeSpectrum.zeroLocus s' = PrimeSpectrum.zeroLocus ↑(Ideal.span s ⊓ Ideal.span s')
Defined in
Mathlib.RingTheory.Spectrum.Prime.Basic
Cited by
0 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiring
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Set · cited by 53352SetCommSemiring · cited by 10911CommSemiringSetLike.coe · cited by 8199SetLike.coeIdeal · cited by 4748IdealIdeal.span · cited by 948Ideal.spanPrimeSpectrum · cited by 625PrimeSpectrumPrimeSpectrum.zeroLocus · cited by 164PrimeSpectrum.zeroLocusPrimeSpectrum.zeroLocus_span · cited by 17PrimeSpectrum.zeroLocus_s…PrimeSpectrum.zeroLocus_inf · cited by 2PrimeSpectrum.zeroLocus_i…PrimeSpectrum.union_zeroLocusCITED BYCITES

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