Theorems · Theorem · commutative algebra

Submodule.LinearDisjoint.of_le_of_flat_right

∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] {M N : Submodule R S},
  M.LinearDisjoint N →
    ∀ {M' N' : Submodule R S}, M' ≤ M → N' ≤ N → ∀ [Module.Flat R ↥N] [Module.Flat R ↥M'], M'.LinearDisjoint N'

If M and N are linearly disjoint, M' and N' are submodules of M and N, respectively, such that N and M' are flat, then M' and N' are also linearly disjoint.

Defined in: Mathlib.LinearAlgebra.LinearDisjoint
Cited by: 0 results in Mathlib
Foundations: Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Ring Algebra Module.Flat Module.Flat

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CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Ringstatement and proof · cited by 7,463
Submodulestatement and proof · cited by 7,192
Module.Flatstatement and proof · cited by 279
Submodule.LinearDisjointstatement and proof · cited by 54
Submodule.LinearDisjoint.of_le_left_of_flatproof · cited by 4
Submodule.LinearDisjoint.of_le_right_of_flatproof · cited by 4

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