Theorems · Theorem · ring theory
Subalgebra.op_adjoin
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (s : Set A),
(Algebra.adjoin R s).op = Algebra.adjoin R (MulOpposite.unop ⁻¹' s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · 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
- Set.preimagestatement and proof · cited by 4,946
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- Set.extproof · cited by 2,266
- Subalgebrastatement · cited by 1,353
- MulOppositestatement and proof · cited by 1,135
- NonAssocSemiringproof · cited by 805
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