Theorems · Theorem · commutative algebra
RingHom.isIntegral_of_surjective
∀ {R : Type u_1} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S),
Function.Surjective ⇑f → f.IsIntegral- Cited by
- 7 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- RingHom.IsIntegralstatement · cited by 54
- RingHom.isIntegralElem_mapproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRingproof · cited by 2
- Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRingproof · cited by 2
- exists_integral_inj_algHom_of_fgproof · cited by 1
- exists_integral_inj_algHom_of_quotientproof · cited by 1
- Polynomial.jacobson_bot_of_integral_localizationproof · cited by 0
- Polynomial.comp_C_integral_of_surjective_of_isJacobsonRingproof · cited by 0
- isIntegral_quotientMap_iffproof · cited by 0