Theorems · Theorem · commutative algebra
Polynomial.Monic.free_adjoinRoot
∀ {R : Type u_1} [inst : CommRing R] {g : Polynomial R}, g.Monic → Module.Free R (AdjoinRoot g)- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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
- Polynomialstatement and proof · cited by 5,681
- Module.Freestatement · cited by 597
- Polynomial.Monicstatement and proof · cited by 461
- AdjoinRootstatement · cited by 177
- PowerBasis.basisproof · cited by 54
- Module.Free.of_basisproof · cited by 20
- AdjoinRoot.powerBasis'proof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Monic.exists_splits_mapproof · cited by 2
- Module.Finite.exists_free_surjectiveproof · cited by 1
- Polynomial.Monic.free_quotientproof · cited by 0