Theorems · Definition · commutative algebra
Ideal.adicModuleTopology
{R : Type u_1} →
[inst : CommRing R] → Ideal R → (M : Type u_2) → [inst_1 : AddCommGroup M] → [Module R M] → TopologicalSpace MThe topology on an R-module M associated to an ideal M. Submodules $I^n M$,
written I^n • ⊤ form a basis of neighborhoods of zero.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Idealstatement and proof · cited by 4,748
- ModuleFilterBasis.topologyproof · cited by 3
- Ideal.ringFilterBasisproof · cited by 1
- Ideal.adic_module_basisproof · cited by 0
- RingFilterBasis.moduleFilterBasisproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- WithIdeal.topologicalSpaceModuleproof · cited by 0