Theorems · Theorem · functional analysis
spectrum.isUnit_of_zero_notMem
∀ (R : Type u) {A : Type v} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] {a : A},
0 ∉ spectrum R a → IsUnit aAlias of the forward direction of spectrum.zero_notMem_iff.
- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- IsUnitstatement · cited by 1,602
- spectrumstatement · cited by 510
- spectrum.zero_notMem_iffproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- CFC.isUnit_rpow_iffproof · cited by 2
- cfcHom_isStrictlyPositive_iffproof · cited by 1