Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical.congr_simp
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
(a a_1 : M), a = a_1 → UniqueFactorizationMonoid.radical a = UniqueFactorizationMonoid.radical a_1- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.radicalstatement and proof · cited by 64
Cited by6
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.radical_mul_dvdproof · cited by 1
- UniqueFactorizationMonoid.radical_pow_dvdproof · cited by 0
- UniqueFactorizationMonoid.radical_prodproof · cited by 0
- UniqueFactorizationMonoid.radical_prod_dvdproof · cited by 0
- UniqueFactorizationMonoid.radical_eq_one_iffproof · cited by 0
- natDegree_radical_leproof · cited by 0