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Theorems · Theorem · commutative algebra

Algebra.FiniteType.trans

∀ {R : Type uR} {S : Type uS} {A : Type uA} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Semiring A]
  [inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A],
  Algebra.FiniteType R S → Algebra.FiniteType S A → Algebra.FiniteType R A
Defined in
Mathlib.RingTheory.FiniteType
Cited by
3 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringCommSemiringSemiringAlgebraAlgebraAlgebraIsScalarTower
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RingHom.FiniteType.comp · cited by 3FiniteType.compAlgebra.exists_unramified_of_isUnramifiedAt · cited by 1Algebra.exists_unramified…Algebra.Unramified.comp · cited by 0Unramified.compSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringIsScalarTower · cited by 3896IsScalarTowerAlgebra.FiniteType · cited by 84Algebra.FiniteTypeAlgebra.FiniteType.out · cited by 14FiniteType.outAlgebra.fg_trans' · cited by 2Algebra.fg_trans'FiniteType.transCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.