Resumen de Nontrivially Noetherian C* -algebras
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).
