Theorems · Theorem · commutative algebra
DvdNotUnit.not_isUnit
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p q : M}, DvdNotUnit p q → ¬IsUnit q- Defined in
- Mathlib.Algebra.Prime.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- 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
- DvdNotUnitstatement and proof · cited by 33
- isUnit_iff_dvd_oneproof · cited by 21
- dvd_of_mul_left_dvdproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- DivisorChain.element_of_chain_not_isUnit_of_index_ne_zeroproof · cited by 1
- DivisorChain.eq_second_of_chain_of_prime_dvdproof · cited by 1
- DvdNotUnit.not_unitproof · cited by 0