Theorems · Theorem · ring theory
DivisionRing.nonempty_linearEquiv_of_isSimpleModule
∀ (S : Type u_2) [inst : DivisionRing S] (N : Type u_3) [inst_1 : AddCommGroup N] [inst_2 : Module S N] [IsSimpleModule S N], Nonempty (N ≃ₗ[S] S)
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- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Idealproof · cited by 4,748
- LinearEquivstatement and proof · cited by 3,317
- HasQuotient.Quotientproof · cited by 2,301
- DivisionRingstatement and proof · cited by 1,062
- Ideal.IsMaximalproof · cited by 452
- LinearEquiv.transproof · cited by 298
- IsSimpleModulestatement and proof · cited by 114
- Ideal.IsMaximal.ne_topproof · cited by 42
- IsSimpleOrder.eq_bot_or_eq_topproof · cited by 32
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