Theorems · Definition · commutative algebra
PowerSeries.IsWeierstrassDivision
{A : Type u_1} →
[inst : CommRing A] → PowerSeries A → PowerSeries A → PowerSeries A → Polynomial A → [IsLocalRing A] → PropVersion of PowerSeries.IsWeierstrassDivisionAt for local rings with respect to
its maximal ideal.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext
- Assumes
- CommRingIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- PowerSeriesstatement and proof · cited by 797
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealproof · cited by 297
- PowerSeries.IsWeierstrassDivisionAtproof · cited by 12
Cited by10
Results whose statement or proof uses this declaration.
- PowerSeries.exists_isWeierstrassFactorizationproof · cited by 4
- PowerSeries.IsWeierstrassDivision.elimstatement and proof · cited by 3
- PowerSeries.IsWeierstrassDivision.isUnit_of_map_ne_zerostatement and proof · cited by 2
- PowerSeries.IsWeierstrassFactorization.isWeierstrassDivisionstatement and proof · cited by 1
- PowerSeries.exists_isWeierstrassDivisionstatement · cited by 1
- PowerSeries.isWeierstrassDivision_weierstrassDiv_weierstrassModstatement · cited by 1
- PowerSeries.IsWeierstrassDivision.congr_simpstatement and proof · cited by 1
- PowerSeries.IsWeierstrassDivision.isWeierstrassFactorizationstatement and proof · cited by 1
- PowerSeries.IsWeierstrassDivision.eq_zerostatement and proof · cited by 0
- PowerSeries.IsWeierstrassDivision.uniquestatement and proof · cited by 0