Theorems · Theorem · group theory
SpecialLinearGroup.subsingleton_of_finrank_eq_one
∀ {R : Type u_1} {V : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup V] [inst_2 : Module R V] [Module.Free R V],
Module.finrank R V = 1 → Subsingleton (SpecialLinearGroup R V)If a free module has Module.finrank equal to 1, then its special linear group is trivial.
- Defined in
- Mathlib.LinearAlgebra.SpecialLinearGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- mul_oneproof · cited by 3,885
- Nontrivialproof · cited by 2,416
- Module.finrankstatement and proof · cited by 1,770
- map_zeroproof · cited by 1,614
- LinearEquiv.symmproof · cited by 1,461
- one_smulproof · cited by 1,374
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