Theorems · Theorem · commutative algebra
Ideal.isFiniteRelIndex
∀ {S : Type u_1} [inst : CommRing S] [IsDedekindDomain S] [Module.Free ℤ S] [Module.Finite ℤ S] {I : Ideal S},
I ≠ ⊥ → ∀ (J : Ideal S), (Submodule.toAddSubgroup I).IsFiniteRelIndex (Submodule.toAddSubgroup J)- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Module.Finitestatement and proof · cited by 1,032
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Submodule.toAddSubgroupstatement and proof · cited by 106
- AddSubgroup.FiniteIndexproof · cited by 66
- AddSubgroup.IsFiniteRelIndexstatement · cited by 17
- Ideal.finiteIndexproof · cited by 1
- AddSubgroup.isFiniteRelIndex_of_finiteIndexproof · cited by 1
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