Theorems · Theorem · field theory
Polynomial.Monic.mul_right_eq_zero_iff
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.Monic → ∀ {q : Polynomial R}, p * q = 0 ↔ q = 0- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.Monic.mul_right_ne_zeroproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Monic.isRegularproof · cited by 1
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1
- Polynomial.isUnit_leadingCoeff_mul_right_eq_zero_iffproof · cited by 0