Theorems · Theorem · commutative algebra
Prime.not_isUnit
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p : M}, Prime p → ¬IsUnit p- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitstatement · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Primestatement and proof · cited by 277
Cited by29
Results whose statement or proof uses this declaration.
- Prime.irreducibleproof · cited by 54
- Ideal.isPrime_of_primeproof · cited by 17
- Prime.dvd_of_dvd_powproof · cited by 14
- Prime.not_dvd_oneproof · cited by 6
- FiniteMultiplicity.of_prime_leftproof · cited by 5
- Associated.primeproof · cited by 4
- emultiplicity_powproof · cited by 3
- prime_factors_uniqueproof · cited by 3
- den_dvd_of_is_rootproof · cited by 2
- IsPrimePow.not_isUnitproof · cited by 2
- Nat.Prime.emultiplicity_oneproof · cited by 2
- Finset.emultiplicity_prodproof · cited by 2