Theorems · Theorem · commutative algebra
RingHom.finite_algebraMap
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B],
(algebraMap A B).Finite ↔ Module.Finite A B- Defined in
- Mathlib.RingTheory.Finiteness.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Algebrastatement and proof · cited by 11,388
- Algebra.algebraMapstatement and proof · cited by 4,706
- Module.Finitestatement and proof · cited by 1,032
- RingHom.Finitestatement · cited by 48
- toAlgebra_algebraMapproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂proof · cited by 1
- AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1
- RingHom.Finite.codescendsAlong_faithfullyFlatproof · cited by 0