Theorems · Theorem · commutative algebra
RingHom.IsIntegral.trans
∀ {R : Type u_1} {S : Type u_4} {T : Type u_5} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
(f : R →+* S) (g : S →+* T), f.IsIntegral → g.IsIntegral → (g.comp f).IsIntegral- Cited by
- 9 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- IsScalarTowerproof · cited by 3,896
- RingHom.compstatement and proof · cited by 899
- RingHom.toAlgebraproof · cited by 337
- Algebra.IsIntegralproof · cited by 224
- Algebra.IsIntegral.isIntegralproof · cited by 86
- RingHom.IsIntegralstatement and proof · cited by 54
- IsScalarTower.of_algebraMap_eqproof · cited by 40
- Algebra.IsIntegral.transproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRingproof · cited by 2
- MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRingproof · cited by 2
- exists_integral_inj_algHom_of_fgproof · cited by 1
- exists_integral_inj_algHom_of_quotientproof · cited by 1
- Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐproof · cited by 1
- RingHom.isIntegral_stableUnderCompositionproof · cited by 1
- Polynomial.jacobson_bot_of_integral_localizationproof · cited by 0
- isIntegral_quotientMap_iffproof · cited by 0
- Polynomial.comp_C_integral_of_surjective_of_isJacobsonRingproof · cited by 0