Theorems · Theorem · ring theory

Module.End.algebraMap_isUnit_inv_apply_eq_iff

∀ {R : Type u} (S : Type v) {M : Type w} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] [inst_4 : Module S M] [inst_5 : SMulCommClass S R M] [inst_6 : SMul R S]
  [inst_7 : IsScalarTower R S M] {x : R} (h : IsUnit ((algebraMap R (Module.End S M)) x)) (m m' : M),
  ↑h.unit⁻¹ m = m' ↔ m = x • m'

Defined in

Mathlib.Algebra.Algebra.Basic

Cited by

8 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAddCommMonoidModuleModuleSMulCommClassSMulIsScalarTower