Theorems · Theorem · commutative algebra
RingHom.IsIntegral.to_finite
∀ {R : Type u_1} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
f.IsIntegral → f.FiniteType → f.Finite- Cited by
- 4 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- RingHom.toAlgebraproof · cited by 337
- Algebra.IsIntegralproof · cited by 224
- RingHom.IsIntegralstatement and proof · cited by 54
- RingHom.Finitestatement · cited by 48
- RingHom.FiniteTypestatement and proof · cited by 46
- Algebra.IsIntegral.finiteproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- RingHom.finite_iff_isIntegral_and_finiteTypeproof · cited by 2
- RingHom.Finite.of_isIntegral_of_finiteTypeproof · cited by 0
- exists_finite_inj_algHom_of_fgproof · cited by 0
- MvPolynomial.finite_universalFactorizationMapproof · cited by 0