On a subalgebra of the algebra C([0,1]) whose maximal ideal space is a torus
Leonid Brevdo (1988)
Studia Mathematica
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Leonid Brevdo (1988)
Studia Mathematica
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J. Kahane, W. Żelazko (1968)
Studia Mathematica
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W. Żelazko (1968)
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Richard Crownover (1970)
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Hakan Hedenmalm (1988)
Mathematica Scandinavica
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H. G. Dales, W. Żelazko (2012)
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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...
Richard Crownover (1969)
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Antoni Wawrzyńczyk (2000)
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The class ω(A) of ideals consisting of topological zero divisors of a commutative Banach algebra A is studied. We prove that the maximal ideals of the class ω(A) are of codimension one.
Young Bae Jun, Seok Zun Song (2016)
Discussiones Mathematicae General Algebra and Applications
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The notions of superior subalgebras and (commutative) superior ideals are introduced, and their relations and related properties are investigated. Conditions for a superior ideal to be commutative are provided.
W. Żelazko (2000)
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Let A be a commutative unital Fréchet algebra, i.e. a completely metrizable topological algebra. Our main result states that all ideals in A are closed if and only if A is a noetherian algebra
Larsen, R. (1971)
Portugaliae mathematica
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Maria Fragoulopoulou (1992)
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A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.
George Maltese, Regina Wille-Fier (1988)
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