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Displaying similar documents to “On ϭ-ideals without maximal extension”

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

W. Żelazko (2006)

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We prove that a real or complex unital F-algebra has all maximal left ideals closed if and only if the set of all its invertible elements is open. Consequently, such an algebra also automatically has all maximal right ideals closed.

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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...

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.

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W. Żelazko (2004)

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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.