Theorems · Theorem · ring theory
NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe
∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} [inst : Field R] [inst_1 : Ring A] [inst_2 : Algebra R A]
[inst_3 : SetLike S A] [hSA : NonUnitalSubringClass S A] [hSRA : SMulMemClass S R A] (s : S) (h1 : 1 ∉ s)
(a : Unitization R ↥s),
↑((NonUnitalSubalgebra.unitizationAlgEquiv s h1) a) = (algebraMap R A) a.toProd.1 + ↑a.toProd.2- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- SetLike.coestatement · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- AlgEquivstatement · cited by 1,681
- Subalgebrastatement · cited by 1,353
- SetLikestatement and proof · cited by 1,084
- Algebra.adjoinstatement · cited by 535
- Unitizationstatement and proof · cited by 220
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