Theorems · Theorem · linear algebra

Module.finrank_top_le_finrank_of_isScalarTower

∀ (R : Type u) (S : Type u_1) (M : Type v) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [StrongRankCondition R] [Module.Finite R M] [inst_5 : Semiring S] [inst_6 : Module S M] [inst_7 : Module R S]
  [IsScalarTower R S S] [FaithfulSMul R S] [IsScalarTower R S M], Module.finrank S M ≤ Module.finrank R M

Also see Module.finrank_top_le_finrank_of_isScalarTower_of_free for a version with different typeclass constraints.

Defined in

Mathlib.LinearAlgebra.Dimension.StrongRankCondition

Cited by

4 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleStrongRankConditionModule.FiniteSemiringModuleModuleIsScalarTowerFaithfulSMulIsScalarTower