Theorems · Definition · group theory
IsPrimal
{α : Type u_1} → [Semigroup α] → α → PropAn element a in a semigroup is primal if whenever a is a divisor of b * c, it can be
factored as the product of a divisor of b and a divisor of c.
- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Semigroup
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.
- Semigroupstatement and proof · cited by 202
Cited by16
Results whose statement or proof uses this declaration.
- DecompositionMonoid.primalstatement · cited by 5
- IsRelPrime.dvd_of_dvd_mul_right_of_isPrimalstatement and proof · cited by 2
- IsRelPrime.dvd_of_dvd_mul_left_of_isPrimalstatement and proof · cited by 1
- IsRelPrime.mul_dvd_of_left_isPrimalstatement and proof · cited by 1
- IsRelPrime.mul_dvd_of_right_isPrimalstatement and proof · cited by 1
- DecompositionMonoid.casesOnstatement and proof · cited by 1
- Irreducible.prime_of_isPrimalstatement and proof · cited by 1
- IsUnit.isPrimalstatement · cited by 0
- IsPrimal.mulstatement and proof · cited by 0
- Associates.isPrimal_mkstatement · cited by 0
- decompositionMonoid_iffstatement and proof · cited by 0
- Submonoid.isPrimalproof · cited by 0