Theorems · Theorem · commutative algebra
Submonoid.LocalizationMap.map_prime
∀ {M : Type u_1} {N : Type u_2} [inst : CommMonoidWithZero M] [inst_1 : CommMonoidWithZero N] {S : Submonoid M}
(f : S.LocalizationMap N) {m : M}, Prime m → f m ≠ 0 → ¬IsUnit (f m) → Prime (f m)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Submonoidstatement and proof · cited by 3,086
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- map_mulproof · cited by 1,137
- CommMonoidWithZerostatement and proof · cited by 913
- Primestatement and proof · cited by 277
- Submonoid.LocalizationMapstatement and proof · cited by 147
- mul_mul_mul_commproof · cited by 65
- Submonoid.LocalizationMap.map_unitsproof · cited by 46
- map_dvdproof · cited by 44
- Prime.dvd_or_dvdproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1