Theorems · Theorem · commutative algebra
Transcendental.integralClosure
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [NoZeroDivisors S]
{a : S}, Transcendental R a → Transcendental (↥(integralClosure R S)) a- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Subalgebrastatement · cited by 1,353
- NoZeroDivisorsstatement and proof · cited by 545
- integralClosurestatement and proof · cited by 105
- Transcendentalstatement and proof · cited by 91
- Transcendental.extendScalars_of_isIntegralproof · cited by 2
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