Theorems · Theorem · commutative algebra

Submodule.smul_assoc

∀ {R : Type u} [inst : Semiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Module R A] {M : Type u_1}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module A M] [inst_6 : IsScalarTower R A M] {B : Type u_2}
  [inst_7 : Semiring B] [inst_8 : Module R B] [inst_9 : Module A B] [inst_10 : Module B M]
  [inst_11 : IsScalarTower R A B] [inst_12 : IsScalarTower R B M] [IsScalarTower A B M] (I : Submodule R A)
  (J : Submodule R B) (N : Submodule R M), (I • J) • N = I • J • N

Defined in

Mathlib.Algebra.Algebra.Operations

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringModuleAddCommMonoidModuleModuleIsScalarTowerSemiringModuleModuleModuleIsScalarTowerIsScalarTowerIsScalarTower