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Displaying similar documents to “A characterization of commutative Fréchet algebras with all ideals closed”

Superior subalgebras and ideals of BCK/BCI-algebras

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.

Foldness of Commutative Ideals in BCK-algebras

Celestin Lele, Salissou Moutari (2006)

Discussiones Mathematicae - General Algebra and Applications

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This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.

On the ideal structure of algebras of LMC-algebra valued functions

Jorma Arhippainen (1992)

Studia Mathematica

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Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.

Generators of maximal left ideals in Banach algebras

H. G. Dales, W. Żelazko (2012)

Studia Mathematica

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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...

On ideals consisting of topological zero divisors

Antoni Wawrzyńczyk (2000)

Studia Mathematica

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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.

A characterization of maximal regular ideals in lmc algebras

Maria Fragoulopoulou (1992)

Studia Mathematica

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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.