Theorems · Theorem · commutative algebra

IsTopologicallyNilpotent.add_of_commute

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

If a and b are topologically nilpotent and commute, then a + b is topologically nilpotent.

Defined in

Mathlib.Topology.Algebra.TopologicallyNilpotent

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceRingIsLinearTopology