Theorems · Theorem · commutative algebra
Ideal.annihilator_quotient
∀ {R : Type u_1} [inst : Ring R] {I : Ideal R} [I.IsTwoSided], Module.annihilator R (R ⧸ I) = I- Defined in
- Mathlib.RingTheory.Ideal.Colon
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Module.annihilatorstatement · cited by 61
- Submodule.colon_univproof · cited by 7
- Submodule.annihilator_quotientproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Module.supportDim_quotient_eq_ringKrullDimproof · cited by 3
- IsSimpleModule.annihilator_isMaximalproof · cited by 1
- ModuleCat.exists_isRegular_tfaeproof · cited by 0
- Module.exists_ker_toSpanSingleton_eq_annihilatorproof · cited by 0