Theorems · Theorem · linear algebra

Module.finrank_tensorProduct

∀ {R : Type u} {S : Type u'} {M : Type v} {M' : Type v'} [inst : Semiring R] [inst_1 : CommSemiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M'] [inst_4 : Module R M] [StrongRankCondition R]
  [StrongRankCondition S] [inst_7 : Module S M] [inst_8 : Module S M'] [Module.Free S M'] [inst_10 : Algebra S R]
  [inst_11 : IsScalarTower S R M] [Module.Free R M],
  Module.finrank R (TensorProduct S M M') = Module.finrank R M * Module.finrank S M'

The S-finrank of M ⊗[R] M' is (finrank S M) * (finrank R M').

Defined in

Mathlib.LinearAlgebra.Dimension.Constructions

Cited by

6 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringCommSemiringAddCommMonoidAddCommMonoidModuleStrongRankConditionStrongRankConditionModuleModuleModule.FreeAlgebraIsScalarTowerModule.Free