Theorems · Theorem · commutative algebra
Subalgebra.LinearDisjoint.bot_right
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] (A : Subalgebra R S),
A.LinearDisjoint ⊥The image of R in S is linearly disjoint with any other subalgebras.
- Defined in
- Mathlib.RingTheory.LinearDisjoint
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 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.
Cites12
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
- Submoduleproof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- Subalgebrastatement and proof · cited by 1,353
- Subalgebra.toSubmoduleproof · cited by 141
- Subalgebra.LinearDisjointstatement · cited by 75
- Submodule.LinearDisjointproof · cited by 54
- Algebra.toSubmodule_botproof · cited by 10
- Submodule.LinearDisjoint.one_rightproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Subalgebra.LinearDisjoint.of_finrank_coprime_of_freeproof · cited by 1
- IntermediateField.LinearDisjoint.bot_rightproof · cited by 0
- IntermediateField.LinearDisjoint.self_rightproof · cited by 0