Theorems · Definition · ring theory
Subalgebra.unop
{R : Type u_2} →
{A : Type u_3} →
[inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Algebra R A] → Subalgebra R Aᵐᵒᵖ → Subalgebra R APull a subalgebra back to a subalgebra along MulOpposite.op
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement and proof · cited by 1,353
- MulOppositestatement and proof · cited by 1,135
- Subsemiringproof · cited by 456
- Subalgebra.toSubsemiringproof · cited by 115
- Subsemiring.unopproof · cited by 26
Cited by22
Results whose statement or proof uses this declaration.
- Subalgebra.opEquivproof · cited by 18
- Subalgebra.unop_toSubsemiringstatement and proof · cited by 1
- Subalgebra.opEquiv_symm_applystatement · cited by 0
- Subalgebra.unop_adjoinstatement and proof · cited by 0
- Subalgebra.unop_botstatement · cited by 0
- Subalgebra.unop_iInfstatement · cited by 0
- Subalgebra.unop_iSupstatement · cited by 0
- Subalgebra.unop_infstatement · cited by 0
- Subalgebra.op_le_iffstatement · cited by 0
- Subalgebra.unop_le_unop_iffstatement · cited by 0
- Subalgebra.op_sInfstatement · cited by 0
- Subalgebra.op_sSupstatement · cited by 0