Theorems · Theorem · commutative algebra

IsTopologicallyNilpotent.mul_right

∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : CommRing R] [IsLinearTopology R R] {a : R},
  IsTopologicallyNilpotent a → ∀ (b : R), IsTopologicallyNilpotent (a * b)

If a is topologically nilpotent, then a * b is topologically nilpotent.

Defined in: Mathlib.Topology.Algebra.TopologicallyNilpotent
Cited by: 0 results in Mathlib
Foundations: Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace CommRing IsLinearTopology

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpacestatement and proof · cited by 24,529
CommRingstatement and proof · cited by 17,173
Commute.allproof · cited by 119
IsLinearTopologystatement and proof · cited by 83
IsTopologicallyNilpotentstatement and proof · cited by 22
IsTopologicallyNilpotent.mul_right_of_commuteproof · cited by 1

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.