Theorems · Definition · number theory

ClassGroup.distinctElems

{R : Type u_1} →
  {S : Type u_2} →
    [inst : EuclideanDomain R] →
      [inst_1 : CommRing S] →
        [inst_2 : IsDomain S] →
          [inst_3 : Algebra R S] →
            {abv : AbsoluteValue R ℤ} →
              {ι : Type u_5} →
                [inst_4 : DecidableEq ι] →
                  [inst_5 : Fintype ι] →
                    (bS : Module.Basis ι R S) →
                      (adm : abv.IsAdmissible) → [Infinite R] → Fin (ClassGroup.cardM bS adm).succ ↪ R

In the following results, we need a large set of distinct elements of R.

Defined in

Mathlib.NumberTheory.ClassNumber.Finite

Cited by

4 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

EuclideanDomainCommRingIsDomainAlgebraDecidableEqFintypeInfinite