Theorems · Theorem · commutative algebra
isStronglyTranscendental_mk_of_mem_minimalPrimes
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsReduced S] {x : S},
IsStronglyTranscendental R x → ∀ q ∈ minimalPrimes S, IsStronglyTranscendental R ((Ideal.Quotient.mk q) x)[Stacks Tag 00Q0](https://stacks.math.columbia.edu/tag/00Q0)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Fieldproof · cited by 7,404
- Polynomialproof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.Cproof · cited by 1,598
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.not_isStronglyTranscendental_of_weaklyQuasiFiniteAtproof · cited by 1