Theorems · Theorem · commutative algebra

Submodule.FG.lTensor.directedSystem

∀ (R : Type u) (M : Type u_1) (N : Type u_2) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N],
  DirectedSystem (fun Q => TensorProduct R M ↥↑Q) fun x x_1 hPQ => ⇑(LinearMap.lTensor M (Submodule.inclusion hPQ))

When Q ranges over finitely generated submodules of N, the modules of the form M ⊗[R] Q form a directed system.

Defined in

Mathlib.RingTheory.TensorProduct.DirectLimitFG

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule