Theorems · Theorem · commutative algebra

Submodule.smul_mem

∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] {module_M : Module R M} (p : Submodule R M)
  {x : M} (r : R), x ∈ p → r • x ∈ p

Defined in

Mathlib.Algebra.Module.Submodule.Defs

Cited by

204 results in Mathlib

Foundations

Depth 13 from the axioms, rests on 78 definitions · uses no axioms

Assumes

SemiringAddCommMonoid