Theorems · Theorem · commutative algebra
Irreducible.not_dvd_isUnit
∀ {M : Type u_1} [inst : CommMonoid M] {p u : M}, Irreducible p → IsUnit u → ¬p ∣ u- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- IsUnitstatement and proof · cited by 1,602
- Irreduciblestatement and proof · cited by 496
- Irreducible.not_isUnitproof · cited by 42
- isUnit_of_dvd_unitproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- Irreducible.not_dvd_oneproof · cited by 1
- Irreducible.not_dvd_unitproof · cited by 0
- PadicInt.zmodRepr_units_ne_zeroproof · cited by 0