Theorems · Theorem · commutative algebra
Algebra.PreSubmersivePresentation.ofHasCoeffs_val
∀ {R : Type u_1} {S : Type u_2} {ι : Type u_3} {σ : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : Algebra R S] (P : Algebra.PreSubmersivePresentation R S ι σ) (R₀ : Type u_5) [inst_3 : CommRing R₀]
[inst_4 : Algebra R₀ R] [inst_5 : Algebra R₀ S] [inst_6 : IsScalarTower R₀ R S] [inst_7 : P.HasCoeffs R₀] (i : ι),
(P.ofHasCoeffs R₀).val i =
(Ideal.Quotient.mk (Ideal.span (Set.range (Algebra.Presentation.relationOfHasCoeffs R₀)))) (MvPolynomial.X i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
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- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- Idealstatement · cited by 4,748
- Set.rangestatement · cited by 4,705
- IsScalarTowerstatement and proof · cited by 3,896
- HasQuotient.Quotientstatement · cited by 2,301
- MvPolynomialstatement · cited by 2,140
- Ideal.spanstatement · cited by 948
- Ideal.Quotient.mkstatement · cited by 610
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