Theorems · Theorem · functional analysis
Pi.spectrum_eq
∀ {ι : Type u_1} {R : Type u_4} {κ : ι → Type u_5} [inst : CommSemiring R] [inst_1 : (i : ι) → Ring (κ i)]
[inst_2 : (i : ι) → Algebra R (κ i)] (a : (i : ι) → κ i), spectrum R a = ⋃ i, spectrum R (a i)- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringRingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Set.ofPredproof · cited by 6,101
- Algebra.algebraMapproof · cited by 4,706
- Compl.complproof · cited by 2,925
- Set.iUnionstatement and proof · cited by 2,483
- IsUnitproof · cited by 1,602
- Set.iInterproof · cited by 1,084
- spectrumstatement and proof · cited by 510
Cited by1
Results whose statement or proof uses this declaration.
- cfc_map_piproof · cited by 1