Note on $\alpha $-filters in distributive nearlattices

Ismael Calomino

Displaying similar documents to “Note on $α$ -filters in distributive nearlattices”

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.

$α$ -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.

Relative co-annihilators in lattice equality algebras

Sogol Niazian, Mona Aaly Kologani, Rajab Ali Borzooei (2024)

Mathematica Bohemica

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We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among $\lor$ -irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra $𝔼$ and $𝔽$ a filter of $𝔼$ , we define the set of all $𝔽$ -involutive filters of $𝔼$ and show that by defining some operations on it, it makes a BL-algebra.

Some properties of state filters in state residuated lattices

Michiro Kondo (2021)

Mathematica Bohemica

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We consider properties of state filters of state residuated lattices and prove that for every state filter $F$ of a state residuated lattice $X$ : (1) $F$ ...

$G$ -supplemented property in the lattices

Shahabaddin Ebrahimi Atani (2022)

Mathematica Bohemica

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Let $L$ be a lattice with the greatest element $1$ . Following the concept of generalized small subfilter, we define $g$ -supplemented filters and investigate the basic properties and possible structures of these filters.

Guessing clubs in the generalized club filter

Bernhard König, Paul Larson, Yasuo Yoshinobu (2007)

Fundamenta Mathematicae

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We present principles for guessing clubs in the generalized club filter on $_{κ} λ$ . These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a λ⁺-Suslin-tree using assumptions different from previous constructions. The other application partly solves open problems regarding the cofinality of reflection points for stationary subsets of ${[λ]}^{ℵ ₀}$ .

Filter factors of truncated TLS regularization with multiple observations

Iveta Hnětynková, Martin Plešinger, Jana Žáková (2017)

Applications of Mathematics

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The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems $A x \approx b$ were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of $A$ applied to $b$ . This paper focuses...

$P_{λ}$ -sets and skeletal mappings

Aleksander Błaszczyk, Anna Brzeska (2013)

Colloquium Mathematicae

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We prove that if the topology on the set Seq of all finite sequences of natural numbers is determined by $P_{λ}$ -filters and λ ≤ , then Seq is a $P_{λ}$ -set in its Čech-Stone compactification. This improves some results of Simon and of Juhász and Szymański. As a corollary we obtain a generalization of a result of Burke concerning skeletal maps and we partially answer a question of his.

$0$ -ideals in $0$ -distributive posets

Khalid A. Mokbel (2016)

Mathematica Bohemica

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The concept of a $0$ -ideal in $0$ -distributive posets is introduced. Several properties of $0$ -ideals in $0$ -distributive posets are established. Further, the interrelationships between $0$ -ideals and $α$ -ideals in $0$ -distributive posets are investigated. Moreover, a characterization of prime ideals to be $0$ -ideals in $0$ -distributive posets is obtained in terms of non-dense ideals. It is shown that every $0$ -ideal of a $0$ -distributive meet semilattice is semiprime. Several counterexamples are discussed. ...

Conditional distributivity of overlap functions over uninorms with continuous underlying operators

Hui Liu, Wenle Li (2024)

Kybernetika

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The investigations of conditional distributivity are encouraged by distributive logical connectives and their generalizations used in fuzzy set theory and were brought into focus by Klement in the closing session of Linzs 2000. This paper is mainly devoted to characterizing all pairs $(O, F)$ of aggregation functions that are satisfying conditional distributivity laws, where $O$ is an overlap function, and $F$ is a continuous t-conorm or a uninorm with continuous underlying operators.

$α$ -ideals in $0$ -distributive posets

Khalid A. Mokbel (2015)

Mathematica Bohemica

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The concept of $α$ -ideals in posets is introduced. Several properties of $α$ -ideals in $0$ -distributive posets are studied. Characterization of prime ideals to be $α$ -ideals in $0$ -distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal $I$ of a $0$ -distributive poset is non-dense, then $I$ is an $α$ -ideal. Moreover, it is shown that the set of all $α$ -ideals $α Id (P)$ of a poset $P$ with $0$ forms a complete lattice. A result analogous to separation theorem for...

Displaying similar documents to “Note on α -filters in distributive nearlattices”

Displaying similar documents to “Note on $α$ -filters in distributive nearlattices”