Theorems · Inductive type · commutative algebra
AddIrreducible
{M : Type u_1} → [AddMonoid M] → M → PropAddIrreducible p states that p is not an additive unit and cannot be written as a sum of
additive non-units.
[Wikidata Q2989575](https://www.wikidata.org/wiki/Q2989575)
- Defined in
- Mathlib.Algebra.Group.Irreducible.Defs
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement · cited by 2,864
Cited by26
Results whose statement or proof uses this declaration.
- addIrreducible_iffstatement and proof · cited by 6
- AddIrreducible.isAddUnit_or_isAddUnitstatement and proof · cited by 4
- not_addIrreducible_zerostatement · cited by 3
- addIrreducible_mem_addSubmonoidClosure_subsetstatement and proof · cited by 2
- AddIrreducible.eq_zero_or_eq_zerostatement and proof · cited by 1
- AddIrreducible.not_evenstatement and proof · cited by 1
- addIrreducible_addUnits_addstatement · cited by 1
- addIrreducible_add_addUnitsstatement · cited by 1
- addIrreducible_add_isAddUnitstatement and proof · cited by 1
- addIrreducible_isAddUnit_addstatement and proof · cited by 1
- addIrreducible_subset_of_addSubmonoidClosure_eq_topstatement and proof · cited by 1
- AddIrreducible.not_isAddUnitstatement and proof · cited by 1