Theorems · Theorem · functional analysis
spectrum.not_isUnit_of_zero_mem
∀ (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_mem_iff.
- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- CommSemiringRingAlgebra
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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_mem_iffproof · cited by 4
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