Theorems · Definition · ring theory
Algebra.botEquiv
(F : Type u_1) → (R : Type u_2) → [inst : Field F] → [inst_1 : Semiring R] → [Nontrivial R] → [inst_3 : Algebra F R] → ↥⊥ ≃ₐ[F] F
The bottom subalgebra is isomorphic to the field.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Bot.botstatement · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- AlgEquivstatement · cited by 1,681
- Subalgebrastatement · cited by 1,353
- Algebra.botEquivOfInjectiveproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- IntermediateField.botEquivproof · cited by 14
- Polynomial.IsSplittingField.liftproof · cited by 2
- IsAlgClosed.nonempty_algEquiv_or_of_finrank_eq_twoproof · cited by 1
- Algebra.botEquiv_symm_applystatement and proof · cited by 0
- Polynomial.lift_of_splitsproof · cited by 0
- JacobsonNoether.exists_separable_and_not_isCentral'proof · cited by 0