Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.center_eq_range_scalar
∀ {R : Type u_1} {n : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R],
Subgroup.center (GL n R) = (Matrix.GeneralLinearGroup.scalar n).rangeThe center of GL n R is the image of Rˣ.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- mul_commproof · cited by 2,262
- Units.valproof · cited by 1,966
- IsEmptyproof · cited by 759
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- MonoidHom.rangestatement and proof · cited by 314
- Matrix.diagonalproof · cited by 314
Cited by6
Results whose statement or proof uses this declaration.
- Matrix.ProjGenLinGroup.mk_eq_mk_iffproof · cited by 0
- UpperHalfPlane.forall_smul_eq_self_iff_mem_centerproof · cited by 0
- Matrix.ProjGenLinGroup.mk_scalarproof · cited by 0
- Matrix.SpecialLinearGroup.toGL_mem_center_iffproof · cited by 0
- Matrix.GeneralLinearGroup.map_center_leproof · cited by 0
- Matrix.GeneralLinearGroup.center_eq_range_unitsproof · cited by 0