Theorems · Theorem · commutative algebra
Irreducible.prime_of_isPrimal
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {a : M}, Irreducible a → IsPrimal a → Prime a- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- Primestatement · cited by 277
- Irreducible.ne_zeroproof · cited by 45
- Irreducible.not_isUnitproof · cited by 42
- IsPrimalstatement and proof · cited by 13
- of_irreducible_mulproof · cited by 5
- IsUnit.mul_right_dvdproof · cited by 4
- IsUnit.mul_left_dvdproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Irreducible.primeproof · cited by 4