Theorems · Theorem · commutative algebra
card_classGroup_eq_one
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsPrincipalIdealRing R],
Fintype.card (ClassGroup R) = 1The class number of a principal ideal domain is 1.
- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Unitsproof · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- Fintype.cardstatement · cited by 1,386
- nonZeroDivisorsproof · cited by 895
- FractionalIdealproof · cited by 423
- FractionRingproof · cited by 200
- IsPrincipalIdealRingstatement and proof · cited by 131
- ClassGroupstatement and proof · cited by 50
- Fintype.card_eq_one_iffproof · cited by 11
- ClassGroup.mk_eq_one_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- card_classGroup_eq_one_iffproof · cited by 2