Theorems · Theorem · commutative algebra
IsAlgebraic.of_finite
∀ (R : Type u_3) {A : Type u_4} [inst : CommRing R] [Nontrivial R] [inst_2 : Ring A] [inst_3 : Algebra R A] (e : A)
[Module.Finite R A], IsAlgebraic R e- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement and proof · cited by 2,416
- Module.Finitestatement and proof · cited by 1,032
- IsAlgebraicstatement · cited by 163
- IsIntegral.isAlgebraicproof · cited by 18
- IsIntegral.of_finiteproof · cited by 16
Cited by8
Results whose statement or proof uses this declaration.
- Field.finSepDegree_eq_finrank_of_isSeparableproof · cited by 7
- Field.finSepDegree_eq_finrank_iffproof · cited by 2
- IntermediateField.isAlgebraic_iSupproof · cited by 1
- isSplittingField_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- Differential.differentialAlgebraFiniteDimensionalproof · cited by 0
- IsLocalRing.exists_adjoin_eq_topproof · cited by 0
- NumberField.adjoin_eq_top_of_infinitePlace_ltproof · cited by 0