Theorems · Theorem · commutative algebra

Module.End.mem_center_iff

∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M]
  {f : Module.End R M}, f ∈ Set.center (Module.End R M) ↔ ∃ α, ∃ (hα : α ∈ Set.center R), f = Module.End.smulLeft α hα

Defined in

Mathlib.LinearAlgebra.FreeModule.Basic

Cited by

4 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleModule.Free