Theorems · Theorem · commutative algebra
Submodule.annihilator_smul
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(N : Submodule R M), N.annihilator • N = ⊥- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- eq_bot_iffproof · cited by 159
- Submodule.annihilatorstatement · cited by 42
- Submodule.smul_leproof · cited by 20
- Submodule.mem_annihilatorproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.eq_bot_of_eq_ideal_smul_of_le_jacobson_annihilatorproof · cited by 4
- Submodule.annihilator_mulproof · cited by 1