Theorems · Theorem · group theory
Matrix.ProjGenLinGroup.mk_eq_one
∀ {n : Type u_1} {R : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R] {g : GL n R},
Matrix.ProjGenLinGroup.mk g = 1 ↔ g ∈ Subgroup.center (GL n R)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- Subgroup.centerstatement and proof · cited by 121
- Matrix.ProjGenLinGroupstatement · cited by 23
- MonoidHom.mem_kerproof · cited by 22
- Matrix.ProjGenLinGroup.mkstatement · cited by 19
- Matrix.ProjGenLinGroup.ker_mkproof · cited by 2
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