Documentation

Mathlib.Algebra.GroupWithZero.Action.Center

The center of a group with zero #

def Subgroup.centerUnitsEquivUnitsCenter (Gā‚€ : Type u_1) [GroupWithZero Gā‚€] :
ↄ(center G₀ˣ) ā‰ƒ* (ↄ(Submonoid.center Gā‚€))Ė£

For a group with zero, the center of the units is the same as the units of the center.

Instances For
    @[simp]
    theorem Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coe (Gā‚€ : Type u_1) [GroupWithZero Gā‚€] (u : (ↄ(Submonoid.center Gā‚€))Ė£) :
    ↑↑((centerUnitsEquivUnitsCenter Gā‚€).symm u) = ↑↑u
    @[simp]
    theorem Subgroup.val_centerUnitsEquivUnitsCenter_apply_coe (Gā‚€ : Type u_1) [GroupWithZero Gā‚€] (a : ↄ(center G₀ˣ)) :
    ↑↑((centerUnitsEquivUnitsCenter Gā‚€) a) = ↑↑a