The spectral theory of posets and its applications to -algebras

Author:
A. H. Dooley

Journal:
Trans. Amer. Math. Soc. **224** (1976), 143-155

MSC:
Primary 46L05; Secondary 06A10

DOI:
https://doi.org/10.1090/S0002-9947-1976-0417796-6

MathSciNet review:
0417796

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Abstract: This paper uses methods from the spectral theory of partially ordered sets to clarify and extend some recent results concerning approximately finite-dimensional -algebras. An extremely explicit description is obtained of the Jacobson topology on the primitive ideal space, and it is shown that this topology has a basis of quasi-compact open sets. In addition, the main results of [4] are proved using only elementary means.

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DOI:
https://doi.org/10.1090/S0002-9947-1976-0417796-6

Article copyright:
© Copyright 1976
American Mathematical Society