Nontrivially Noetherian C* -algebras
- Autores: Taylor Hines, Erik Walsberg
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 111, Nº 1, 2012, págs. 135-146
- Idioma: inglés
- DOI: 10.7146/math.scand.a-15219
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Resumen
We say that a C∗-algebra is Noetherian if it satisfies the ascending chain condition for two-sided closed ideals. A nontrivially Noetherian C∗-algebra is one with infinitely many ideals. Here, we show that nontrivially Noetherian C∗-algebras exist, and that a separable C∗-algebra is Noetherian if and only if it contains countably many ideals and has no infinite strictly ascending chain of primitive ideals. Furthermore, we prove that every Noetherian C∗-algebra has a finite-dimensional center. Where possible, we extend results about the ideal structure of C∗-algebras to Artinian C∗-algebras (those satisfying the descending chain condition for closed ideals).
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