Theorems · Theorem · commutative algebra
AdjoinRoot.isDomain_of_prime
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R}, Prime f → IsDomain (AdjoinRoot f)- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement · cited by 2,196
- Ideal.spanproof · cited by 948
- Primestatement and proof · cited by 277
- AdjoinRootstatement · cited by 177
- Prime.ne_zeroproof · cited by 47
- Ideal.span_singleton_primeproof · cited by 27
- Ideal.Quotient.isDomain_iff_primeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.adjoin.powerBasis'_minpoly_genproof · cited by 0