Theorems · Theorem · field theory
IsLocalization.isAlgebraic
∀ {R : Type u} (S : Type u_1) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Nontrivial R]
(M : Submonoid R) [IsLocalization M S], Algebra.IsAlgebraic R S- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- Nontrivialstatement and proof · cited by 2,416
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
Cited by2
Results whose statement or proof uses this declaration.
- finTrdeg_iff_trdegproof · cited by 4
- exists_integral_multiplesproof · cited by 1