On non-removable ideals in commutative locally convex algebras
W. Żelazko (1983)
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W. Żelazko (1983)
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Vladimír Müller (1984)
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V. Müller (1982)
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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
L. Lindahl (1975)
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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.
V. Müller (1982)
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Vladimír Müller (1984)
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Hugo Peimbert, Wiesław Żelazko (1985)
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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.
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.
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.