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Theorems · Theorem · commutative algebra

Algebra.Generators.C_mul_X_sub_one_mem_ker

∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (r : R)
  [inst_3 : IsLocalization.Away r S],
  MvPolynomial.C r * MvPolynomial.X () - 1 ∈ (Algebra.Generators.localizationAway S r).ker
Defined in
Mathlib.RingTheory.Extension.Presentation.Basic
Cited by
1 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraIsLocalization.Away
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.Generators.cMulXSubOneCotangent · cited by 11Generators.cMulXSubOneCot…Algebra.Generators.cMulXSubOneCotangent_eq · cited by 0Generators.cMulXSubOneCot…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRingHom · cited by 10189RingHomFinsupp · cited by 5255FinsuppIdeal · cited by 4748IdealMvPolynomial · cited by 2140MvPolynomialMvPolynomial.X · cited by 552MvPolynomial.XMvPolynomial.C · cited by 400MvPolynomial.CIsLocalization.Away · cited by 218IsLocalization.AwayAlgebra.Generators.Ring · cited by 133Generators.RingAlgebra.Generators.ker · cited by 46Generators.kerAlgebra.Generators.localizationAway · cited by 23Generators.localizationAw…Algebra.Presentation.relation_mem_ker · cited by 9Presentation.relation_mem…Algebra.Presentation.localizationAway · cited by 5Presentation.localization…Generators.C_mul_X_sub_one_me…CITED BYCITES

Cites15

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Cited by2

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