Normal restrictions of the noncofinal ideal on
Pierre Matet (2013)
Fundamenta Mathematicae
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We discuss the problem of whether there exists a restriction of the noncofinal ideal on that is normal.
Pierre Matet (2013)
Fundamenta Mathematicae
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We discuss the problem of whether there exists a restriction of the noncofinal ideal on that is normal.
Ali Rezaei Aliabad, F. Azarpanah, M. Namdari (2004)
Commentationes Mathematicae Universitatis Carolinae
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We prove that a Hausdorff space is locally compact if and only if its topology coincides with the weak topology induced by . It is shown that for a Hausdorff space , there exists a locally compact Hausdorff space such that . It is also shown that for locally compact spaces and , if and only if . Prime ideals in are uniquely represented by a class of prime ideals in . -compact spaces are introduced and it turns out that a locally compact space is -compact if and only...
Marta Frankowska, Andrzej Nowik (2011)
Colloquium Mathematicae
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We prove that the ideal (a) defined by the density topology is not generated. This answers a question of Z. Grande and E. Strońska.
F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2008)
Colloquium Mathematicae
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Let be the socle of C(X). It is shown that each prime ideal in is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points....
Barnabás Farkas, Lajos Soukup (2009)
Commentationes Mathematicae Universitatis Carolinae
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Given an ideal on let () be minimum of the cardinalities of infinite (uncountable) maximal -almost disjoint subsets of . We show that if is a summable ideal; but for any tall density ideal including the density zero ideal . On the other hand, you have for any analytic -ideal , and for each density ideal . For each ideal on denote and the unbounding and dominating numbers of where iff . We show that and for each analytic -ideal . Given a Borel...
B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky (2007)
Studia Mathematica
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It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in , including one that has not been studied before. The proofs use various methods...
Piotr Zakrzewski (2015)
Commentationes Mathematicae Universitatis Carolinae
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We give a classical proof of the theorem stating that the -ideal of meager sets is the unique -ideal on a Polish group, generated by closed sets which is invariant under translations and ergodic.
Ali Yassine, Mohammad Javad Nikmehr, Reza Nikandish (2024)
Czechoslovak Mathematical Journal
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Let be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of -ideals and a subclass of -absorbing primary ideals. A proper ideal of is called strongly 1-absorbing primary if for all nonunit elements such that , it is either or . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings over which every semi-primary ideal is strongly 1-absorbing primary, and rings over which...
Masato Kurihara (1999)
Journal of the European Mathematical Society
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In this paper, for a totally real number field we show the ideal class group of is trivial. We also study the -component of the ideal class group of the cyclotomic -extension.
Khalid A. Mokbel (2016)
Mathematica Bohemica
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The concept of a -ideal in -distributive posets is introduced. Several properties of -ideals in -distributive posets are established. Further, the interrelationships between -ideals and -ideals in -distributive posets are investigated. Moreover, a characterization of prime ideals to be -ideals in -distributive posets is obtained in terms of non-dense ideals. It is shown that every -ideal of a -distributive meet semilattice is semiprime. Several counterexamples are discussed. ...
Stefania Gabelli (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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If is a domain with the ascending chain condition on (integral) invertible ideals, then the group of its invertible ideals is generated by the set of maximal invertible ideals. In this note we study some properties of and we prove that, if is a free group on , then is a locally factorial Krull domain.