Theorems · Theorem · number theory
Algebra.isUnramifiedIn_bot
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsDomain R]
[IsDomain S] [FaithfulSMul R S] [CharZero R] [Algebra.IsIntegral R S], Algebra.IsUnramifiedIn S ⊥In characteristic zero, the zero ideal is unramified in an integral domain extension.
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- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- CharZerostatement and proof · cited by 932
- Ideal.IsPrimeproof · cited by 827
- FaithfulSMulstatement and proof · cited by 340
- Ideal.LiesOverproof · cited by 272
- Algebra.IsIntegralstatement and proof · cited by 224
- Algebra.IsUnramifiedInstatement · cited by 9
- Ideal.eq_bot_of_liesOver_botproof · cited by 5
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