Theorems · Theorem · commutative algebra

IsTopologicallyNilpotent.mul_right_of_commute

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

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

Defined in

Mathlib.Topology.Algebra.TopologicallyNilpotent

Cited by

1 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceRingIsLinearTopology