Theorems · Definition · commutative algebra

Ideal.basisSpanSingleton

{ι : Type u_1} →
  {R : Type u_2} →
    {S : Type u_3} →
      [inst : CommSemiring R] →
        [inst_1 : CommRing S] →
          [IsDomain S] →
            [inst_3 : Algebra R S] → Module.Basis ι R S → {x : S} → x ≠ 0 → Module.Basis ι R ↥(Ideal.span {x})

A basis on S gives a basis on Ideal.span {x}, by multiplying everything by x.

Defined in

Mathlib.RingTheory.Ideal.Basis

Cited by

4 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommRingIsDomainAlgebra