c-ideals in complemented posets

Ivan Chajda; Miroslav Kolařík; Helmut Länger

Displaying similar documents to “c-ideals in complemented posets”

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...

Note on $α$ -filters in distributive nearlattices

Ismael Calomino (2019)

Mathematica Bohemica

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In this short paper we introduce the notion of $α$ -filter in the class of distributive nearlattices and we prove that the $α$ -filters of a normal distributive nearlattice are strongly connected with the filters of the distributive nearlattice of the annihilators.

Some observations on filters with properties defined by open covers

Rodrigo Hernández-Gutiérrez, Paul J. Szeptycki (2015)

Commentationes Mathematicae Universitatis Carolinae

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We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of $𝒫 (ω)$ with the Cantor set topology.

$α$ -filters and $α$ -order-ideals in distributive quasicomplemented semilattices

Ismael Calomino, Sergio A. Celani (2021)

Commentationes Mathematicae Universitatis Carolinae

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We introduce some particular classes of filters and order-ideals in distributive semilattices, called $α$ -filters and $α$ -order-ideals, respectively. In particular, we study $α$ -filters and $α$ -order-ideals in distributive quasicomplemented semilattices. We also characterize the filters-congruence-cokernels in distributive quasicomplemented semilattices through $α$ -order-ideals.

When does the Katětov order imply that one ideal extends the other?

Paweł Barbarski, Rafał Filipów, Nikodem Mrożek, Piotr Szuca (2013)

Colloquium Mathematicae

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We consider the Katětov order between ideals of subsets of natural numbers (" $\leq_{K}$ ") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which $\leq_{K} \Rightarrow ⊑$ for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).

Generalized prime $D$ -filters of distributive lattices

A.P. Phaneendra Kumar, M. Sambasiva Rao, K. Sobhan Babu (2021)

Archivum Mathematicum

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The concept of generalized prime $D$ -filters is introduced in distributive lattices. Generalized prime $D$ -filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime $D$ -filters is introduced in distributive lattices and properties of minimal prime $D$ -filters are then studied with respect to congruences. Some topological properties of the space of all prime $D$ -filters of a distributive lattice are also studied.

$C (X)$ can sometimes determine $X$ without $X$ being realcompact

Melvin Henriksen, Biswajit Mitra (2005)

Commentationes Mathematicae Universitatis Carolinae

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As usual $C (X)$ will denote the ring of real-valued continuous functions on a Tychonoff space $X$ . It is well-known that if $X$ and $Y$ are realcompact spaces such that $C (X)$ and $C (Y)$ are isomorphic, then $X$ and $Y$ are homeomorphic; that is $C (X)$ $X$ . The restriction to realcompact spaces stems from the fact that $C (X)$ and $C (υ X)$ are isomorphic, where $υ X$ is the (Hewitt) realcompactification of $X$ . In this note, a class of locally compact spaces $X$ that includes properly the class of locally...