### The Ideal Transform and Overrings of an Integral Domain.

Jim Brewer (1968)

Mathematische Zeitschrift

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Jim Brewer (1968)

Mathematische Zeitschrift

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Wolfgang Schwarz, Hans-Günter Zimmer (1996)

Mathematische Zeitschrift

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L.J. Jr. Ratliff (1984/85)

Mathematische Zeitschrift

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Piotr Kalemba (2015)

Open Mathematics

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The ideal (v0) is known in the literature and is naturally linked to the structure [ω]ω. We consider some natural counterpart of the ideal (v0) related in an analogous way to the structure Dense(ℚ) and investigate its combinatorial properties. By the use of the notion of ideal type we prove that under CH this ideal is isomorphic to (v0).

Thomas C. Craven (1982)

Mathematische Zeitschrift

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Scheja, Günter, Storch, Uwe (1996)

Beiträge zur Algebra und Geometrie

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Rosłanowski, Andrzej, Shelah, Saharon (1997)

Journal of Applied Analysis

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Voskoglou, M.G. (1990)

Publications de l'Institut Mathématique. Nouvelle Série

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G.B. WAGNER (1969)

Mathematische Annalen

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Azzouz Cherrabi, Abderrahim Miri (1999)

Extracta Mathematicae

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Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2013)

Commentationes Mathematicae Universitatis Carolinae

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We show that the ideal of nowhere dense subsets of rationals cannot be extended to an analytic P-ideal, ${F}_{\sigma}$ ideal nor maximal P-ideal. We also consider a problem of extendability to a non-meager P-ideals (in particular, to maximal P-ideals).