Theorems · Theorem · commutative algebra
Polynomial.Monic.free_quotient
∀ {R : Type u_1} [inst : CommRing R] {g : Polynomial R}, g.Monic → Module.Free R (Polynomial R ⧸ Ideal.span {g})An unwrapped version of AdjoinRoot.free_of_monic for better discoverability.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Idealstatement · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.spanstatement · cited by 948
- Module.Freestatement · cited by 597
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.Monic.free_adjoinRootproof · cited by 3
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