Theorems · Theorem · commutative algebra
Prime.not_dvd_one
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p : M}, Prime p → ¬p ∣ 1- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- CommMonoidWithZero
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
- Primestatement and proof · cited by 277
- Prime.not_isUnitproof · cited by 29
- isUnit_of_dvd_oneproof · cited by 18
Cited by6
Results whose statement or proof uses this declaration.
- Prime.dvd_prod_iffproof · cited by 2
- Prime.exists_mem_multiset_dvdproof · cited by 2
- Ideal.exists_isMaximal_dvd_of_dvd_absNormproof · cited by 2
- PowerSeries.maximalIdeal_eq_span_Xproof · cited by 1
- IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_twoproof · cited by 1
- isCoprime_of_gcd_eq_one_of_FLTproof · cited by 0