Theorems · Theorem · commutative algebra
Submodule.LinearDisjoint.one_right
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] (M : Submodule R S),
M.LinearDisjoint 1The image of R in S is linearly disjoint with any other submodules.
- Defined in
- Mathlib.LinearAlgebra.LinearDisjoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapproof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Bot.botproof · cited by 4,720
- TensorProductproof · cited by 2,545
- LinearEquiv.injectiveproof · cited by 162
- Subalgebra.toSubmoduleproof · cited by 141
- Submodule.LinearDisjointstatement · cited by 54
Cited by2
Results whose statement or proof uses this declaration.
- Subalgebra.LinearDisjoint.bot_rightproof · cited by 3
- Submodule.LinearDisjoint.of_right_le_one_of_flatproof · cited by 0