Theorems · Theorem · ring theory

Module.End.mem_subalgebraCenter_iff

∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [Module.Free R M] [inst_4 : CommSemiring S] [inst_5 : Module S M] [inst_6 : SMulCommClass R S M]
  [inst_7 : Algebra S R] [inst_8 : IsScalarTower S R M] {f : Module.End R M},
  f ∈ Subalgebra.center S (Module.End R M) ↔ ∃ α, ∃ (hα : α ∈ Subalgebra.center S 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.FreeCommSemiringModuleSMulCommClassAlgebraIsScalarTower