Theorems · Theorem · commutative algebra
Module.mem_support_iff_of_finite
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{p : PrimeSpectrum R} [Module.Finite R M], p ∈ Module.support R M ↔ Module.annihilator R M ≤ p.asIdeal- Defined in
- Mathlib.RingTheory.Support
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submoduleproof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Idealstatement and proof · cited by 4,748
- Finset.prodproof · cited by 2,356
- mul_commproof · cited by 2,262
Cited by4
Results whose statement or proof uses this declaration.
- Module.support_eq_zeroLocusproof · cited by 10
- Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobsonproof · cited by 2
- IsSMulRegular.subsingleton_linearMap_iffproof · cited by 2
- Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimesproof · cited by 1