Some properties of Lorenzen ideal systems

Aleka Kalapodi; Angeliki Kontolatou; Jiří Močkoř

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

Normal restrictions of the noncofinal ideal on $P_{κ} (λ)$

Pierre Matet (2013)

Fundamenta Mathematicae

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We discuss the problem of whether there exists a restriction of the noncofinal ideal on $P_{κ} (λ)$ that is normal.

Erratum to $(δ, 2)$ -primary ideals of a commutative ring

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

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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 $I = f (x) K [x] \cap R [x]$ 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 $I = f (x) K [x] \cap R [x]$ we have: – $I^{- 1} \cap K [x] = (I :_{K (x)} I)$ . – If there exists...

On wsq-primary ideals

Emel Aslankarayiğit Uğurlu, El Mehdi Bouba, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

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We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $Q$ a proper ideal of $R$ . The proper ideal $Q$ is said to be a weakly strongly quasi-primary ideal if whenever $0 \neq a b \in Q$ for some $a, b \in R$ , then $a^{2} \in Q$ or $b \in \sqrt{Q} .$ Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero...