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.
S. Bogdanović (1985)
Matematički Vesnik
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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.
W. Żelazko (2000)
Studia Mathematica
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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
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...
E. Casas Alvero (1993)
Cours de l'institut Fourier
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Jan Mycielski (1969)
Colloquium Mathematicae
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Wolmer V. Vasconcelos (1967)
Mathematische Zeitschrift
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Sonia Sharma (2010)
Studia Mathematica
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We generalize an important class of Banach spaces, the M-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided M-embedded operator spaces are the operator spaces which are one-sided M-ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension property, Radon-Nikodým property and many more, are retained in the non-commutative setting. We also discuss...
Zandt, Michael (1995)
Beiträge zur Algebra und Geometrie
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J. E. Baumgartner, A. D. Taylor, S. Wagon
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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...
R.W. GILMER (1967)
Mathematische Annalen
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W. Żelazko (2006)
Studia Mathematica
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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.
Sterling K. Berberian (1983)
Mathematische Zeitschrift
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W. Żelazko (1974)
Colloquium Mathematicae
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W. Żelazko (2004)
Studia Mathematica
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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.
Jeppe Christoffer Dyre (1982)
Mathematica Scandinavica
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A. Kwela, P. Zakrzewski (2017)
Commentationes Mathematicae Universitatis Carolinae
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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.
Jan R. Strooker (1966)
Mathematische Zeitschrift
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