Theorems · Theorem · commutative algebra
not_irreducible_of_not_isUnit_of_dvdNotUnit
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p q : M}, ¬IsUnit p → DvdNotUnit p q → ¬Irreducible q- Defined in
- Mathlib.Algebra.Prime.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
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.
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement · cited by 496
- DvdNotUnitstatement and proof · cited by 33
- DvdNotUnit.isUnit_of_irreducible_rightproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- DivisorChain.eq_second_of_chain_of_prime_dvdproof · cited by 1
- not_irreducible_of_not_unit_dvdNotUnitproof · cited by 0