Theorems · Theorem · commutative algebra
Algebra.finite_iff_isIntegral_and_finiteType
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A],
Module.Finite R A ↔ Algebra.IsIntegral R A ∧ Algebra.FiniteType R Afinite = integral + finite type
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- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Module.Finitestatement and proof · cited by 1,032
- Algebra.IsIntegralstatement and proof · cited by 224
- Algebra.FiniteTypestatement and proof · cited by 84
- IsIntegral.of_finiteproof · cited by 16
- Algebra.IsIntegral.finiteproof · cited by 5
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