Theorems · Theorem · commutative algebra

ClassGroup.mk0_eq_one_iff

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDedekindDomain R] {I : Ideal R}
  (hI : I ∈ nonZeroDivisors (Ideal R)), ClassGroup.mk0 ⟨I, hI⟩ = 1 ↔ Submodule.IsPrincipal I

Defined in

Mathlib.RingTheory.ClassGroup.Basic

Cited by

4 results in Mathlib

Foundations

Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainIsDedekindDomain