Theorems · Theorem · commutative algebra

Submodule.sup_smul

∀ {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]
  (I J : Submodule R A) (N : Submodule R M), (I ⊔ J) • N = I • N ⊔ J • N

Defined in

Mathlib.Algebra.Algebra.Operations

Cited by

4 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringModuleAddCommMonoidModuleModuleIsScalarTower