Theorems · Theorem · commutative algebra
Module.annihilator_eq_bot
∀ {R : Type u_4} {M : Type u_5} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M],
Module.annihilator R M = ⊥ ↔ FaithfulSMul R M- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Idealstatement · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- sub_selfproof · cited by 996
- zero_smulproof · cited by 716
- sub_eq_zeroproof · cited by 407
- FaithfulSMulstatement and proof · cited by 340
- le_bot_iffproof · cited by 116
- sub_smulproof · cited by 97
- Module.annihilatorstatement and proof · cited by 61
Cited by2
Results whose statement or proof uses this declaration.
- Module.supportDim_self_eq_ringKrullDimproof · cited by 3
- Ideal.nonempty_inter_nonZeroDivisors_of_faithfulSMulproof · cited by 0