Theorems · Theorem · functional analysis
Unitization.mem_spectrum_inr_of_not_isUnit
∀ {R : Type u_3} {A : Type u_4} [inst : CommRing R] [inst_1 : NonUnitalRing A] [inst_2 : Module R A]
[inst_3 : IsScalarTower R A A] [inst_4 : SMulCommClass R A A] (a : A) (r : R), ¬IsUnit r → r ∈ spectrum R ↑a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- IsUnitstatement and proof · cited by 1,602
- sub_zeroproof · cited by 938
- map_subproof · cited by 565
- spectrumstatement · cited by 510
- NonUnitalRingstatement and proof · cited by 422
Cited by1
Results whose statement or proof uses this declaration.
- Unitization.quasispectrum_eq_spectrum_inrproof · cited by 4