Theorems · Theorem · commutative algebra
not_irreducible_of_not_unit_dvdNotUnit
Deprecated since 2026-08-02Use not_irreducible_of_not_isUnit_of_dvdNotUnit instead.
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p q : M}, ¬IsUnit p → DvdNotUnit p q → ¬Irreducible qAlias of not_irreducible_of_not_isUnit_of_dvdNotUnit.
- Defined in
- Mathlib.Algebra.Prime.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitstatement · cited by 1,602
- CommMonoidWithZerostatement · cited by 913
- Irreduciblestatement · cited by 496
- DvdNotUnitstatement · cited by 33
- not_irreducible_of_not_isUnit_of_dvdNotUnitproof · cited by 2
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