Theorems · Definition · commutative algebra
HahnSeries.ofPowerSeries
(Γ : Type u_1) →
(R : Type u_2) →
[inst : Semiring R] →
[inst_1 : Semiring Γ] →
[inst_2 : PartialOrder Γ] → [inst_3 : IsStrictOrderedRing Γ] → PowerSeries R →+* HahnSeries Γ RCasts a power series as a Hahn series with coefficients from a strictly ordered semiring.
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- RingHom.compproof · cited by 899
- PowerSeriesstatement · cited by 797
- RingEquiv.symmproof · cited by 567
- HahnSeriesstatement · cited by 528
- RingEquiv.toRingHomproof · cited by 150
- Nat.castAddMonoidHomproof · cited by 16
- HahnSeries.toPowerSeriesproof · cited by 10
- HahnSeries.embDomainRingHomproof · cited by 2
Cited by47
Results whose statement or proof uses this declaration.
- LaurentSeries.coe_algebraMapstatement · cited by 5
- HahnSeries.ofPowerSeries_Xstatement · cited by 5
- LaurentSeries.coeff_coe_powerSeriesstatement · cited by 3
- LaurentSeries.intValuation_le_iff_coeff_lt_eq_zerostatement and proof · cited by 3
- HahnSeries.ofPowerSeries_Cstatement · cited by 3
- HahnSeries.ofPowerSeries_X_powstatement and proof · cited by 3
- LaurentSeries.single_order_mul_powerSeriesPartstatement and proof · cited by 3
- LaurentSeries.powerSeries_as_subringproof · cited by 3
- LaurentSeries.val_le_one_iff_eq_coestatement and proof · cited by 3
- LaurentSeries.valuation_X_powstatement and proof · cited by 3
- LaurentSeries.valuation_le_iff_coeff_lt_eq_zeroproof · cited by 3
- PowerSeries.coe_powstatement and proof · cited by 3