Theorems · Theorem · commutative algebra

Module.IsStablyFree.exist_free_prod

∀ (R : Type u) [inst : Ring R] (M : Type v) [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.IsStablyFree R M],
  ∃ N x x_1, ∃ (_ : Module.Finite R N) (_ : Module.Free R N), Module.Free R (M × N)

Defined in: Mathlib.Algebra.Module.StablyFree.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 17 from the axioms · uses propext, Quot.sound
Assumes: Ring AddCommGroup Module Module.IsStablyFree

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
Module.Finitestatement · cited by 1,032
Module.Freestatement · cited by 597
Module.IsStablyFreestatement and proof · cited by 8

Cited by2

Results whose statement or proof uses this declaration.

Module.IsStablyFree.equivproof · cited by 3
Module.free_of_isStablyFree_of_invertibleproof · cited by 0