Theorems · Theorem · commutative algebra
RingHom.Finite.to_isIntegral
∀ {R : Type u_1} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S}, f.Finite → f.IsIntegral[Stacks Tag 00GK](https://stacks.math.columbia.edu/tag/00GK)
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- RingHomstatement and proof · cited by 10,189
- Top.topproof · cited by 9,680
- RingHom.IsIntegralstatement · cited by 54
- RingHom.Finitestatement and proof · cited by 48
- Module.Finite.fg_topproof · cited by 28
- IsIntegral.of_mem_of_fgproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- RingHom.finite_iff_isIntegral_and_finiteTypeproof · cited by 2
- RingHom.IsIntegral.of_finiteproof · cited by 1
- exists_leadingCoeff_pow_smul_mem_conductorproof · cited by 1