Theorems · Theorem · commutative algebra
AdjoinRoot.of.injective_of_degree_ne_zero
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R} [IsDomain R],
f.degree ≠ 0 → Function.Injective ⇑(AdjoinRoot.of f)- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- le_antisymmproof · cited by 2,068
- Polynomial.Cproof · cited by 1,598
- WithBotstatement and proof · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- AdjoinRootstatement and proof · cited by 177
- injective_iff_map_eq_zeroproof · cited by 62
- AdjoinRoot.ofstatement and proof · cited by 52
Cited by1
Results whose statement or proof uses this declaration.
- AdjoinRoot.noZeroSMulDivisors_of_prime_of_degree_ne_zeroproof · cited by 1