Theorems · Theorem · number theory
bijective_algebraMap_int_of_finite_of_unramified
∀ {𝒪 : Type u_2} [inst : CommRing 𝒪] [Module.Finite ℤ 𝒪] [Algebra.Unramified ℤ 𝒪] [IsDomain 𝒪] [FaithfulSMul ℤ 𝒪],
Function.Bijective ⇑(algebraMap ℤ 𝒪)If 𝒪 is a domain that is a finite and unramified extension of ℤ, then 𝒪 = ℤ.
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- Foundations
- Depth 320 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Module.finrankproof · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- CharZeroproof · cited by 932
- Function.Bijectivestatement · cited by 863
- IsDedekindDomainproof · cited by 668
- NumberFieldproof · cited by 653
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