Theorems · Theorem · commutative algebra
PowerSeries.spanFinrank_eq_spanFinrank_map_constantCoeff_of_X_notMem_of_fg_of_isPrime
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal (PowerSeries R)} [I.IsPrime],
PowerSeries.X ∉ I → I.FG → Submodule.spanFinrank I = Submodule.spanFinrank (Ideal.map PowerSeries.constantCoeff I)- Defined in
- Mathlib.RingTheory.PowerSeries.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIdeal.IsPrime
Around this declaration
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Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- Set.Finiteproof · cited by 1,814
- le_transproof · cited by 985
- Ideal.spanproof · cited by 948
- Ideal.IsPrimestatement and proof · cited by 827
- PowerSeriesstatement and proof · cited by 797
- Ideal.mapstatement and proof · cited by 692
Cited by1
Results whose statement or proof uses this declaration.