Dense Ideals of Group Algebras.
V. Losert, E. Kotzmann, H. Rindler (1979)
Mathematische Annalen
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V. Losert, E. Kotzmann, H. Rindler (1979)
Mathematische Annalen
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Wend Werner (1991)
Mathematische Annalen
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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.
Melahat Almus, David P. Blecher, Charles John Read (2012)
Studia Mathematica
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This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently...
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...
Sterling K. Berberian (1983)
Mathematische Zeitschrift
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Yngve Domar (1959)
Mathematica Scandinavica
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O. Reynov (1981)
Studia Mathematica
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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.
Yngve Domar (1972)
Mathematische Zeitschrift
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J.T. Burnham (1974)
Monatshefte für Mathematik
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Stanisław Kasjan, Maja Sędłak (2008)
Colloquium Mathematicae
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Given a quiver Q, a field K and two (not necessarily admissible) ideals I, I' in the path algebra KQ, we study the problem when the factor algebras KQ/I and KQ/I' of KQ are isomorphic. Sufficient conditions are given in case Q is a tree extension of a cycle.
Ehrhard Behrends (1988)
Studia Mathematica
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Yılmaz Çeven, Zekiye Çiloğlu (2015)
Discussiones Mathematicae - General Algebra and Applications
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In this paper, using the notion of upper sets, we introduced the notions of complicated BE-Algebras and gave some related properties on complicated, self-distributive and commutative BE-algebras. In a self-distributive and complicated BE-algebra, characterizations of ideals are obtained.
R. Larsen (1969)
Monatshefte für Mathematik
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Jorma Arhippainen, Jukka Kauppi (2013)
Studia Mathematica
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We develop the theory of Segal algebras of commutative C*-algebras, with an emphasis on the functional representation. Our main results extend the Gelfand-Naimark Theorem. As an application, we describe faithful principal ideals of C*-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.