Theorems · Theorem · group theory
prime_mul_iff
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {x y : M},
Prime (x * y) ↔ Prime x ∧ IsUnit y ∨ IsUnit x ∧ Prime y- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
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Cites11
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
- Primestatement and proof · cited by 277
- IsCancelMulZerostatement and proof · cited by 177
- Associated.symmproof · cited by 87
- Prime.irreducibleproof · cited by 54
- associated_mul_unit_leftproof · cited by 8
- of_irreducible_mulproof · cited by 5
- Associated.primeproof · cited by 4
- associated_unit_mul_leftproof · cited by 4
- associated_unit_mul_rightproof · cited by 3
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