Displaying similar documents to “Some properties of Lorenzen ideal systems”

Annihilators in normal autometrized algebras

Ivan Chajda, Jiří Rachůnek (2001)

Czechoslovak Mathematical Journal

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The concepts of an annihilator and a relative annihilator in an autometrized l -algebra are introduced. It is shown that every relative annihilator in a normal autometrized l -algebra 𝒜 is an ideal of 𝒜 and every principal ideal of 𝒜 is an annihilator of 𝒜 . The set of all annihilators of 𝒜 forms a complete lattice. The concept of an I -polar is introduced for every ideal I of 𝒜 . The set of all I -polars is a complete lattice which becomes a two-element chain provided I is prime. The I -polars...

The ideal (a) is not G δ generated

Marta Frankowska, Andrzej Nowik (2011)

Colloquium Mathematicae

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We prove that the ideal (a) defined by the density topology is not G δ generated. This answers a question of Z. Grande and E. Strońska.

A characterization of the meager ideal

Piotr Zakrzewski (2015)

Commentationes Mathematicae Universitatis Carolinae

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We give a classical proof of the theorem stating that the σ -ideal of meager sets is the unique σ -ideal on a Polish group, generated by closed sets which is invariant under translations and ergodic.

On spaces with the ideal convergence property

Jakub Jasinski, Ireneusz Recław (2008)

Colloquium Mathematicae

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Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to I b , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.

Uppers to zero in R [ x ] and almost principal ideals

Keivan Borna, Abolfazl Mohajer-Naser (2013)

Czechoslovak Mathematical Journal

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Let R be an integral domain with quotient field K and f ( x ) a polynomial of positive degree in K [ x ] . In this paper we develop a method for studying almost principal uppers to zero ideals. More precisely, we prove that uppers to zero divisorial ideals of the form I = f ( x ) K [ x ] ∩ R [ x ] are almost principal in the following two cases: – J , the ideal generated by the leading coefficients of I , satisfies J - 1 = R . – I - 1 as the R [ x ] -submodule of K ( x ) is of finite type. Furthermore we prove that for I = f ( x ) K [ x ] ∩ R [ x ] we have: – I - 1 ∩ K [ x ] = ( I : K ( x ) I ) . – If there exists...

More on cardinal invariants of analytic P -ideals

Barnabás Farkas, Lajos Soukup (2009)

Commentationes Mathematicae Universitatis Carolinae

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Given an ideal ℐ on ω let 𝔞 ( ℐ ) ( 𝔞 ¯ ( ℐ ) ) be minimum of the cardinalities of infinite (uncountable) maximal ℐ -almost disjoint subsets of [ ω ] ω . We show that 𝔞 ( ℐ h ) > ω if ℐ h is a summable ideal; but 𝔞 ( 𝒵 μ → ) = ω for any tall density ideal 𝒵 μ → including the density zero ideal 𝒵 . On the other hand, you have 𝔟 ≤ 𝔞 ¯ ( ℐ ) for any analytic P -ideal ℐ , and 𝔞 ¯ ( 𝒵 μ → ) ≤ 𝔞 for each density ideal 𝒵 μ → . For each ideal ℐ on ω denote 𝔟 ℐ and 𝔡 ℐ the unbounding and dominating numbers of 〈 ω ω , ≤ ℐ 〉 where f ≤ ℐ g iff { n ∈ ω : f ( n ) > g ( n ) } ∈ ℐ . We show that 𝔟 ℐ = 𝔟 and 𝔡 ℐ = 𝔡 for each analytic P -ideal ℐ . Given a Borel...