Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.center_eq_range_units
Deprecated since 2026-02-08Use Matrix.GeneralLinearGroup.center_eq_range_scalar instead.
∀ {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).rangeAlias of Matrix.GeneralLinearGroup.center_eq_range_scalar.
The center of GL n R is the image of Rˣ.
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- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement · cited by 17,173
- Fintypestatement · cited by 7,736
- Matrixstatement · cited by 4,303
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- Matrix.GeneralLinearGroupstatement · cited by 556
- MonoidHom.rangestatement · cited by 314
- Subgroup.centerstatement · cited by 121
- Matrix.GeneralLinearGroup.scalarstatement · cited by 18
- Matrix.GeneralLinearGroup.center_eq_range_scalarproof · cited by 6
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