Theorems · Theorem · commutative algebra
Polynomial.lifts_iff_ringHom_rangeS
∀ {R : Type u} [inst : Semiring R] {S : Type v} [inst_1 : Semiring S] {f : R →+* S} (p : Polynomial S),
p ∈ Polynomial.lifts f ↔ p ∈ (Polynomial.mapRingHom f).rangeS- Defined in
- Mathlib.Algebra.Polynomial.Lifts
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapproof · cited by 806
- Subsemiringstatement · cited by 456
- Polynomial.mapRingHomstatement · cited by 98
- RingHom.rangeSstatement · cited by 47
- Polynomial.liftsstatement · cited by 35
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.lifts_iff_coeff_liftsproof · cited by 10
- Polynomial.erase_mem_liftsproof · cited by 0