Theorems · Theorem · commutative algebra

UniqueFactorizationMonoid.radical_eq_one_iff

∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
  {a : M}, UniqueFactorizationMonoid.radical a = 1 ↔ a = 0 ∨ IsUnit a

Defined in

Mathlib.RingTheory.Radical.Basic

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroNormalizationMonoidUniqueFactorizationMonoid