Theorems · Theorem · commutative algebra
IsSMulRegular.notMem_of_mem_minimalPrimes
∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_3} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {x : R},
IsSMulRegular M x → ∀ {p : Ideal R}, p ∈ (Module.annihilator R M).minimalPrimes → x ∉ p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Iff.notproof · cited by 489
- smul_smulproof · cited by 360
- IsSMulRegularstatement and proof · cited by 128
- Ideal.minimalPrimesstatement and proof · cited by 74
- Module.annihilatorstatement and proof · cited by 61
- Module.mem_annihilatorproof · cited by 14
- IsSMulRegular.right_eq_zero_of_smulproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobsonproof · cited by 2