Theorems · Theorem · commutative algebra
Ideal.IsIntegral.mem_minimalPrimes_map_under
∀ {R : Type u_1} [inst : CommRing R] {A : Type u_3} [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.IsIntegral R A] (I : Ideal A) [I.IsPrime], I ∈ (Ideal.map (algebraMap R A) (Ideal.under R I)).minimalPrimes- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapstatement and proof · cited by 692
- Algebra.IsIntegralstatement and proof · cited by 224
- Ideal.understatement and proof · cited by 170
- not_le_of_gtproof · cited by 97
- Ideal.minimalPrimesstatement · cited by 74
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