Theorems · Theorem · commutative algebra

IsTopologicallyNilpotent.mul_left

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

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

Defined in

Mathlib.Topology.Algebra.TopologicallyNilpotent

Cited by

2 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceCommRingIsLinearTopology