Theorems · Theorem · commutative algebra
Submodule.annihilator_quotient
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Submodule R M},
Module.annihilator R (M ⧸ N) = N.colon Set.univ- Defined in
- Mathlib.RingTheory.Ideal.Colon
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Set.univstatement and proof · cited by 3,945
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Submodule.mapproof · cited by 614
- Submodule.mkQproof · cited by 232
- Ideal.extproof · cited by 131
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.annihilator_quotientproof · cited by 4
- Module.support_quotientproof · cited by 1