Theorems · Theorem · ring theory
Algebra.map_bot
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : Semiring B] [inst_4 : Algebra R B] (f : A →ₐ[R] B), Subalgebra.map f ⊥ = ⊥- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Bot.botstatement and proof · cited by 4,720
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement · cited by 1,353
- AlgHom.toLinearMapproof · cited by 254
- Subalgebra.toSubmoduleproof · cited by 141
- Subalgebra.mapstatement and proof · cited by 90
- Submodule.map.congr_simpproof · cited by 75
- Algebra.toSubmodule_botproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.map_botproof · cited by 1