Theorems · Theorem · commutative algebra
addIrreducible_iff
∀ {M : Type u_1} [inst : AddMonoid M] {p : M},
AddIrreducible p ↔ ¬IsAddUnit p ∧ ∀ ⦃a b : M⦄, p = a + b → IsAddUnit a ∨ IsAddUnit b- Defined in
- Mathlib.Algebra.Group.Irreducible.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- IsAddUnitstatement and proof · cited by 215
- AddIrreduciblestatement and proof · cited by 24
- AddIrreducible.isAddUnit_or_isAddUnitproof · cited by 4
- AddIrreducible.not_isAddUnitproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- not_addIrreducible_zeroproof · cited by 3
- AddEquiv.addIrreducible_iffproof · cited by 1
- addIrreducible_addUnits_addproof · cited by 1
- addIrreducible_add_addUnitsproof · cited by 1
- AddSubmonoid.closure_addIrreducibleproof · cited by 0
- addIrreducible_or_factorproof · cited by 0