Theorems · Theorem · commutative algebra
PowerSeries.maximalIdeal_eq_span_X
∀ {k : Type u_2} [inst : Field k], IsLocalRing.maximalIdeal (PowerSeries k) = Ideal.span {PowerSeries.X}The maximal ideal of k⟦X⟧ is generated by X.
- Defined in
- Mathlib.RingTheory.PowerSeries.Inverse
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Ideal.spanstatement and proof · cited by 948
- PowerSeriesstatement and proof · cited by 797
- map_subproof · cited by 565
- Ideal.IsMaximalproof · cited by 452
- sub_eq_zeroproof · cited by 407
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- PowerSeries.Xstatement and proof · cited by 183
- PowerSeries.constantCoeffproof · cited by 126
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.ker_coeff_eq_max_idealproof · cited by 0