A theorem of Gel'fand-Mazur type

Hung Le Pham

Hung Le Pham

Studia Mathematica, Tome 192 (2009), p. 81-88 / Harvested from The Polish Digital Mathematics Library

Résumé

Denote by any set of cardinality continuum. It is proved that a Banach algebra A with the property that for every collection $a_{α} : α \in \subset A$ there exist α ≠ β ∈ such that $a_{α} \in a_{β} A^{}$ is isomorphic to $⨁_{i = 1}^{r} (ℂ [X] / X^{d_{i}} ℂ [X]) \oplus E$ , where $d ₁, . . ., d_{r} \in ℕ$ , and E is either $X ℂ [X] / X^{d ₀} ℂ [X]$ for some d₀ ∈ ℕ or a 1-dimensional $⨁_{i = 1}^{r} ℂ [X] / X^{d_{i}} ℂ [X]$ -bimodule with trivial right module action. In particular, ℂ is the unique non-zero prime Banach algebra satisfying the above condition.

Publié le : 2009-01-01

Zbl 1176.46045

EUDML-ID : urn:eudml:doc:284875

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     title = {A theorem of Gel'fand-Mazur type},
     journal = {Studia Mathematica},
     volume = {192},
     year = {2009},
     pages = {81-88},
     zbl = {1176.46045},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-1-6}
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Hung Le Pham. A theorem of Gel'fand-Mazur type. Studia Mathematica, Tome 192 (2009) pp. 81-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-1-6/