Theorems · Theorem · ring theory

Module.End.mem_subsemiringCenter_iff

∀ {R : Type u_1} {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 ∈ Subsemiring.center (Module.End R M) ↔ ∃ α, ∃ (hα : α ∈ Subsemiring.center R), f = Module.End.smulLeft α hα

Defined in

Mathlib.Algebra.Central.End

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleModule.Free