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$𝒲$ -completeness and fixpoint properties

Marcel Erné (1988)

Archivum Mathematicum

$𝒵$ -distributive function lattices

Marcel Erné (2013)

Mathematica Bohemica

It is known that for a nonempty topological space $X$ and a nonsingleton complete lattice $Y$ endowed with the Scott topology, the partially ordered set $[X, Y]$ of all continuous functions from $X$ into $Y$ is a continuous lattice if and only if both $Y$ and the open set lattice $𝒪 X$ are continuous lattices. This result extends to certain classes of $𝒵$ -distributive lattices, where $𝒵$ is a subset system replacing the system $𝒟$ of all directed subsets (for which the $𝒟$ -distributive complete lattices are just the continuous...

$𝒩$ -fuzzy ideals in ordered semigroups.

Khan, Asghar, Jun, Young Bae, Shabir, Muhammad (2009)

International Journal of Mathematics and Mathematical Sciences

$*$ -median

Bohumil Šmarda (1996)

Mathematica Slovaca

$ℱ$ -multipliers and the localization of MV-algebras.

Buşneag, Dumitru, Piciu, Dana (2003)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

$\forall_{n}$ -theories of Boolean algebras

Jan Waszkiewicz (1974)

Colloquium Mathematicae

$𝒩$ -structures applied to closed ideals in BCH-algebras.

Jun, Young Bae, Öztürk, Mehmet Ali, Roh, Eun Hwan (2010)

International Journal of Mathematics and Mathematical Sciences

$𝒩$ -subalgebras in BCK/BCI-algebras based on point $𝒩$ -structures.

Jun, Young Bae, Kang, Min Su, Park, Chul Hwan (2010)

International Journal of Mathematics and Mathematical Sciences

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

Khalid A. Mokbel (2016)

Mathematica Bohemica

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.

0-distributive posets

Khalid A. Mokbel, Vilas S. Kharat (2013)

Mathematica Bohemica

Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper $l$ -filter of a poset is contained in a proper semiprime filter, then it is $0$ -distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is shown that...

2-normalization of lattices

Ivan Chajda, W. Cheng, S. L. Wismath (2008)

Czechoslovak Mathematical Journal

Let $τ$ be a type of algebras. A valuation of terms of type $τ$ is a function $v$ assigning to each term $t$ of type $τ$ a value $v (t) \geq 0$ . For $k \geq 1$ , an identity $s \approx t$ of type $τ$ is said to be $k$ -normal (with respect to valuation $v$ ) if either $s = t$ or both $s$ and $t$ have value $\geq k$ . Taking $k = 1$ with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called $k$ -normal (with respect to the valuation $v$ ) if all its identities are $k$ -normal. For any variety $V$ , there is a least...

...-definierbare Funktionen auf Peanoalgebren.

Gerd Mitschke (1972)

Archiv für mathematische Logik und Grundlagenforschung

“Hidden variables” on concrete logics (extensions)

Pavel Pták (1987)

Commentationes Mathematicae Universitatis Carolinae

$ℓ$ -многообразия без независимого базиса тождеств. II.

N.Ya. Medvedev (1985)

Mathematica Slovaca

Łukasiewicz tribes are absolutely sequentially closed bold algebras

Roman Frič (2002)

Czechoslovak Mathematical Journal

We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean $M V$ -algebra) can be uniquely extended to a sequentially continuous measure on the generated Łukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on Łukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields...

$𝔪$ -poproduct of lattices

Zuzana Ladzianska (1985)

Mathematica Slovaca

(Pre)order preserving additive homomorphisms of (pre)ordered commutative semigroups into real numbers

Tomáš Kepka, Petr Němec (2012)

Acta Universitatis Carolinae. Mathematica et Physica

...-Strukturen.

Niels Schwartz (1978)

Mathematische Zeitschrift

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

Ismael Calomino, Sergio A. Celani (2021)

Commentationes Mathematicae Universitatis Carolinae

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.

$α$ -ideals and annihilator ideals in 0-distributive lattices

Y. S. Pawar, S. S. Khopade (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In a 0-distributive lattice sufficient conditions for an $α$ -ideal to be an annihilator ideal and prime ideal to be an $α$ -ideal are given. Also it is proved that the images and the inverse images of $α$ -ideals are $α$ -ideals under annihilator preserving homomorphisms.

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