Theorems · Theorem · commutative algebra
Ideal.Filtration.inf_submodule
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {I : Ideal R}
(F F' : I.Filtration M), (F ⊓ F').submodule = F.submodule ⊓ F'.submodule- Defined in
- Mathlib.RingTheory.Filtration
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 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.
Cites12
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
- Submodulestatement · cited by 7,192
- Polynomialstatement · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Subalgebrastatement · cited by 1,353
- Submodule.extproof · cited by 204
- PolynomialModulestatement and proof · cited by 76
- Ideal.Filtrationstatement and proof · cited by 32
- reesAlgebrastatement · cited by 12
- Ideal.Filtration.submodulestatement · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.Filtration.submoduleInfHomproof · cited by 1