Theorems · Theorem · commutative algebra
AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk
Deprecated since 2026-03-02Use AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapMk_mk instead.
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (f p : Polynomial R),
(AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapMk I f)
((Ideal.Quotient.mk (Ideal.map (AdjoinRoot.mk f) (Ideal.map Polynomial.C I))) ((AdjoinRoot.mk f) p)) =
(DoubleQuot.quotQuotMk (Ideal.map Polynomial.C I) (Ideal.span {f})) pAlias of AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapMk_mk.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Idealstatement · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Polynomial.Cstatement · cited by 1,598
- RingEquivstatement · cited by 1,147
- Ideal.spanstatement · cited by 948
- Ideal.mapstatement · cited by 692
- Ideal.Quotient.mkstatement · cited by 610
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