Theorems · Theorem · commutative algebra
Polynomial.comp_C_integral_of_surjective_of_isJacobsonRing
∀ {R : Type u_1} [inst : CommRing R] [IsJacobsonRing R] {S : Type u_2} [inst_2 : Field S] (f : Polynomial R →+* S),
Function.Surjective ⇑f → (f.comp Polynomial.C).IsIntegral- Defined in
- Mathlib.RingTheory.Jacobson.Ring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsJacobsonRingField
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Cites22
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
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- HasQuotient.Quotientproof · cited by 2,301
- Polynomial.Cstatement and proof · cited by 1,598
- RingHom.compstatement and proof · cited by 899
- Ideal.Quotient.mkproof · cited by 610
- Ideal.IsMaximalproof · cited by 452
- RingHom.kerproof · cited by 363
- RingHom.IsIntegralstatement and proof · cited by 54
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