Theorems · Theorem · commutative algebra

TensorProduct.add_smul

∀ {R : Type u_1} {R'' : Type u_5} [inst : CommSemiring R] [inst_1 : Semiring R''] {M : Type u_7} {N : Type u_8}
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : Module R'' M] [inst_5 : Module R M]
  [inst_6 : Module R N] [inst_7 : SMulCommClass R R'' M] (r s : R'') (x : TensorProduct R M N),
  (r + s) • x = r • x + s • x

Defined in

Mathlib.LinearAlgebra.TensorProduct.Defs

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAddCommMonoidAddCommMonoidModuleModuleModuleSMulCommClass