Theorems · Theorem · commutative algebra

Module.not_finite_of_infinite_basis

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Nontrivial R]
  {ι : Type u_3} [Infinite ι] (b : Module.Basis ι R M), ¬Module.Finite R M

Defined in

Mathlib.RingTheory.Finiteness.Cardinality

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleNontrivialInfinite