Theorems · Theorem · ring theory
Algebra.adjoin_empty
∀ (R : Type uR) (A : Type uA) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A], R[] = ⊥
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Bot.botstatement · cited by 4,720
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- GaloisConnection.l_botproof · cited by 63
- Algebra.gcproof · cited by 7
Cited by10
Results whose statement or proof uses this declaration.
- fg_adjoin_of_finiteproof · cited by 9
- Algebra.EssFiniteType.of_isLocalizationproof · cited by 5
- IsCyclotomicExtension.iff_union_singleton_oneproof · cited by 2
- IsCyclotomicExtension.singleton_zero_of_bot_eq_topproof · cited by 2
- MvPolynomial.supported_emptyproof · cited by 1
- Subalgebra.fg_botproof · cited by 0
- Subalgebra.induction_on_adjoinproof · cited by 0
- Polynomial.lift_of_splitsproof · cited by 0
- Normal.of_isSplittingFieldproof · cited by 0
- Polynomial.isSplittingField_Cproof · cited by 0