On the Characterization of Primitive Ideals in Enveloping Algebras.
Ronald S. Irving, Lance W. Small (1980)
Mathematische Zeitschrift
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Displaying similar documents to “Primitive Ideals of Certain Noetherian Algebras.”
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Mart Abel (2005)
Banach Center Publications
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It is shown that every unital σ-complete topologically primitive strongly galbed Hausdorff algebra in which all elements are bounded is central
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In 1971, Grauert and Remmert proved that a commutative, complex, Noetherian Banach algebra is necessarily finite-dimensional. More precisely, they proved that a commutative, complex Banach algebra has finite dimension over ℂ whenever all the closed ideals in the algebra are (algebraically) finitely generated. In 1974, Sinclair and Tullo obtained a non-commutative version of this result. In 1978, Ferreira and Tomassini improved the result of Grauert and Remmert by showing that...
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Alternative noetherian Banach algebras.
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Sinclair and Tullo [6] proved that noetherian Banach algebras are finite-dimensional. In [3], Grabiner studied noetherian Banach modules. In this paper, we are concerned with alternative noetherian Banach algebras. Combining techniques from [3] with techniques and the result from [6], we prove that every alternative noetherian Banach algebra is finite-dimensional.