On non-removable ideals in commutative locally convex algebras
W. Żelazko (1983)
Studia Mathematica
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W. Żelazko (1983)
Studia Mathematica
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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.
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.
Vladimir Müller (1991)
Collectanea Mathematica
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An ideal in a commutative topological algebra with separately continuous multiplication is non-removable if and only if it consists locally of joint topological divisors of zero. Also, any family of non-removable ideals can be removed simultanously.
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.
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...
Keiji Izuchi (1976)
Studia Mathematica
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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.
W. Żelazko (2006)
Colloquium Mathematicae
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We construct an example as announced in the title. We also indicate all right, left and two-sided ideals in this example.
W. Żelazko (2005)
Studia Mathematica
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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.
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.
William Dietrich (1975)
Fundamenta Mathematicae
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Simões, Marilda A. (1987)
Portugaliae mathematica
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