Theorems · Theorem · commutative algebra
isSMulRegular_iff_right_eq_zero_of_smul
∀ {R : Type u_1} {M : Type u_3} [inst : AddGroup M] [inst_1 : DistribSMul R M] {r : R},
IsSMulRegular M r ↔ ∀ (m : M), r • m = 0 → m = 0- Defined in
- Mathlib.Algebra.Regular.SMul
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupDistribSMul
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.
- AddGroupstatement and proof · cited by 4,410
- sub_selfproof · cited by 996
- sub_eq_zeroproof · cited by 407
- smul_subproof · cited by 142
- IsSMulRegularstatement and proof · cited by 128
- DistribSMulstatement and proof · cited by 117
- IsSMulRegular.right_eq_zero_of_smulproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- isSMulRegular_quotient_iff_mem_of_smul_memproof · cited by 2
- IsSMulRegular.of_right_eq_zero_of_smulproof · cited by 2
- isSMulRegular_submodule_iff_right_eq_zero_of_smulproof · cited by 1
- isSMulRegular_iff_mem_nonZeroSMulDivisorsproof · cited by 1