Theorems · Definition · algebraic geometry
minimalPrimes.equivIrreducibleComponents
(R : Type u) → [inst : CommSemiring R] → ↑(minimalPrimes R) ≃o (↑(irreducibleComponents (PrimeSpectrum R)))ᵒᵈ
Zero loci of minimal prime ideals of R are irreducible components in Spec R and any
irreducible component is a zero locus of some minimal prime ideal.
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- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- OrderDualstatement · cited by 927
- OrderIsostatement and proof · cited by 874
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- irreducibleComponentsstatement · cited by 35
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