Theorems · Theorem · commutative algebra
IsAdjoinRootMonic.finrank
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
(h : IsAdjoinRootMonic S f) [StrongRankCondition R], Module.finrank R S = f.natDegree- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Polynomialstatement and proof · cited by 5,681
- Module.finrankstatement · cited by 1,770
- Polynomial.natDegreestatement · cited by 1,105
- StrongRankConditionstatement and proof · cited by 286
- IsAdjoinRootMonicstatement and proof · cited by 35
- PowerBasis.finrankproof · cited by 14
- IsAdjoinRootMonic.powerBasisproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalRing.minpoly_map_residueproof · cited by 1
- finrank_quotient_span_eq_natDegree'proof · cited by 0