Theorems · Definition · ring theory
Subalgebra.op
{R : Type u_2} →
{A : Type u_3} →
[inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Algebra R A] → Subalgebra R A → Subalgebra R AᵐᵒᵖPull a subalgebra back to an opposite subalgebra along MulOpposite.unop
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, 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.
- 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.opproof · cited by 43
- Subalgebra.algebraMap_memproof · cited by 28
Cited by34
Results whose statement or proof uses this declaration.
- Subalgebra.opEquivproof · cited by 18
- Subalgebra.linearEquivOpstatement · cited by 3
- Subalgebra.mopAlgEquivOpstatement · cited by 2
- Subalgebra.algEquivOpMopstatement · cited by 2
- Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_opstatement and proof · cited by 2
- Subalgebra.op_toSubsemiringstatement and proof · cited by 1
- Subalgebra.mem_opstatement · cited by 0
- Subalgebra.mopAlgEquivOp_apply_coestatement · cited by 0
- Subalgebra.mopAlgEquivOp_symm_applystatement · cited by 0
- Subalgebra.algEquivOpMop_applystatement · cited by 0
- Subalgebra.algEquivOpMop_symm_apply_coestatement · cited by 0
- Subalgebra.opEquiv_applystatement · cited by 0