Theorems · Theorem · commutative algebra
Ideal.isoBaseOfIsPrincipal_apply
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] {I : Ideal R} [hprinc : Submodule.IsPrincipal I] (hI : I ≠ ⊥)
(x : R), ↑((Ideal.isoBaseOfIsPrincipal hI) x) = x * Submodule.IsPrincipal.generator I- Defined in
- Mathlib.RingTheory.Ideal.IsPrincipal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- LinearEquivstatement · cited by 3,317
- IsDomainstatement and proof · cited by 2,196
- Submodule.IsPrincipalstatement and proof · cited by 129
- Submodule.IsPrincipal.generatorstatement · cited by 56
- Ideal.isoBaseOfIsPrincipalstatement · cited by 4
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