Theorems · Theorem · ring theory
NonUnitalStarSubalgebra.unitization_injective
∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} [inst : Field R] [inst_1 : StarRing R] [inst_2 : Ring A]
[inst_3 : StarRing A] [inst_4 : Algebra R A] [inst_5 : StarModule R A] [inst_6 : SetLike S A]
[hSA : NonUnitalSubringClass S A] [hSRA : SMulMemClass S R A] [inst_7 : StarMemClass S A] (s : S),
1 ∉ s → Function.Injective ⇑(NonUnitalStarSubalgebra.unitization s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- zero_addproof · cited by 2,366
- StarRingstatement and proof · cited by 1,686
- map_zeroproof · cited by 1,614
- SetLikestatement and proof · cited by 1,084
- StarModulestatement and proof · cited by 570
- Unitizationstatement · cited by 220
- StarAlgHomstatement · cited by 215
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