Theorems · Theorem · commutative algebra
Associates.isAtom_iff
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {p : Associates M},
p ≠ 0 → (IsAtom p ↔ Irreducible p)- Defined in
- Mathlib.RingTheory.ChainOfDivisors
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- mul_oneproof · cited by 3,885
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- Associatedproof · cited by 296
- IsUnit.unitproof · cited by 252
- Associatesstatement and proof · cited by 210
- IsCancelMulZerostatement and proof · cited by 177
- IsAtomstatement and proof · cited by 130
Cited by2
Results whose statement or proof uses this declaration.
- DivisorChain.second_of_chain_is_irreducibleproof · cited by 3
- map_prime_of_factor_orderIsoproof · cited by 2