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Theorems · Definition · commutative algebra

PowerSeries.IsWeierstrassFactorization

{A : Type u_1} → [inst : CommRing A] → PowerSeries A → Polynomial A → PowerSeries A → [IsLocalRing A] → Prop

Version of PowerSeries.IsWeierstrassFactorizationAt for local rings with respect to its maximal ideal.

Defined in
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation
Cited by
13 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.

PowerSeries.isWeierstrassFactorization_weierstrassDistinguished_weierstrassUnit · cited by 5PowerSeries.isWeierstrass…PowerSeries.IsWeierstrassFactorization.elim · cited by 5IsWeierstrassFactorizatio…PowerSeries.exists_isWeierstrassFactorization · cited by 4PowerSeries.exists_isWeie…PowerSeries.IsWeierstrassFactorization.map_ne_zero · cited by 3IsWeierstrassFactorizatio…PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision · cited by 1IsWeierstrassFactorizatio…PowerSeries.IsWeierstrassDivision.isWeierstrassFactorization · cited by 1IsWeierstrassDivision.isW…PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map · cited by 1IsWeierstrassFactorizatio…PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map · cited by 0IsWeierstrassFactorizatio…PowerSeries.IsWeierstrassFactorization.unique · cited by 0IsWeierstrassFactorizatio…PowerSeries.weierstrassDistinguished_mul · cited by 0PowerSeries.weierstrassDi…PowerSeries.weierstrassDistinguished_smul · cited by 0PowerSeries.weierstrassDi…PowerSeries.weierstrassUnit_mul · cited by 0PowerSeries.weierstrassUn…PowerSeries.weierstrassUnit_smul · cited by 0PowerSeries.weierstrassUn…CommRing · cited by 17173CommRingPolynomial · cited by 5681PolynomialPowerSeries · cited by 797PowerSeriesIsLocalRing · cited by 339IsLocalRingIsLocalRing.maximalIdeal · cited by 297IsLocalRing.maximalIdealPowerSeries.IsWeierstrassFactorizationAt · cited by 11PowerSeries.IsWeierstrass…PowerSeries.IsWeierstrassFact…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by13

Results whose statement or proof uses this declaration.