Theorems · Theorem · commutative algebra
QuotSMulTop.mem_annihilator
∀ {R : Type u_2} [inst : CommRing R] (M : Type u_1) [inst_1 : AddCommGroup M] [inst_2 : Module R M] (x : R),
x ∈ Module.annihilator R (QuotSMulTop x M)- Defined in
- Mathlib.RingTheory.QuotSMulTop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement · cited by 4,748
- Submodule.Quotient.mkproof · cited by 184
- Submodule.pointwiseDistribMulActionstatement · cited by 105
- Module.annihilatorstatement · cited by 61
- QuotSMulTopstatement and proof · cited by 46
- Module.mem_annihilatorproof · cited by 14
- Submodule.Quotient.mk_surjectiveproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- ModuleCat.projectiveDimension_quotSMulTop_eq_succ_of_isSMulRegularproof · cited by 1