Theorems · Definition · functional analysis

Unitization.unitsFstOne_mulEquiv_quasiregular

(R : Type u_1) →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : NonUnitalSemiring A] →
        [inst_2 : Module R A] →
          [inst_3 : IsScalarTower R A A] →
            [inst_4 : SMulCommClass R A A] → ↥(Unitization.unitsFstOne R A) ≃* (PreQuasiregular A)ˣ

If A is a non-unital R-algebra, then the subgroup of units of Unitization R A whose scalar part is 1 : R (i.e., Unitization.unitsFstOne) is isomorphic to the group of units of PreQuasiregular A.

Defined in

Mathlib.Algebra.Algebra.Spectrum.Quasispectrum

Cited by

5 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalSemiringModuleIsScalarTowerSMulCommClass