When a unital F-algebra has all maximal left (right) ideals closed?

W. Żelazko

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Displaying similar documents to “When a unital F-algebra has all maximal left (right) ideals closed?”

On ϭ-ideals without maximal extension

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A characterization of Q-algebras of type F

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We prove that a real or complex unital F-algebra is a Q-algebra if and only if all its maximal one-sided ideals are closed.

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A characterization of F-algebras with all one-sided ideals closed

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We prove that a real or complex F-algebra has all left and right ideals closed if and only if it is noetherian.

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Filtrations by Complete Ideals and Applications

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Some new ideals of sets on the real line

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Generators of maximal left ideals in Banach algebras

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...

Minimal and maximal ideals in rings with involution.

Birkenmeier, Gary F., Groenewald, Nico J., Heatherly, Henry E. (1997)

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Combinatorics of ideals --- selectivity versus density

A. Kwela, P. Zakrzewski (2017)

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This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.

Structural properties of ideals

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CONTENTSPreface.............................................................................................. 5Chapter I. Preliminaries................................................................. 61. Notation and terminology.......................................................... 62. Results from the literature......................................................... 93. Definitions and basic properties.............................................. 11Chapter II. Subnormality and...