The Ohm type properties for multiplication ideals.
Ali, Majid M. (1996)
Beiträge zur Algebra und Geometrie
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Ali, Majid M. (1996)
Beiträge zur Algebra und Geometrie
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Weinert, H.J., Sen, M.K., Adhikari, M.R. (1996)
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Bohumil Šmarda (1980)
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Keiji Izuchi (1976)
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Kondo, Michiro (2001)
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James J. Madden, Niels Schwartz (1997)
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Experience shows that in geometric situations the separating ideal associated with two orderings of a ring measures the degree of tangency of the corresponding ultrafilters of semialgebraic sets. A related notion of separating ideals is introduced for pairs of valuations of a ring. The comparison of both types of separating ideals helps to understand how a point on a surface is approached by different half-branches of curves.
David Rudd (1975)
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Jaromír Duda (1991)
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Jörg Brendle, Diego Alejandro Mejía (2014)
Fundamenta Mathematicae
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The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even...