Relative co-annihilators in lattice equality algebras

Sogol Niazian; Mona Aaly Kologani; Rajab Ali Borzooei

Displaying similar documents to “Relative co-annihilators in lattice equality algebras”

$G$ -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.

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) $F$ ...

An investigation on the $n$ -fold IVRL-filters in triangle algebras

Saeide Zahiri, Arsham Borumand Saeid (2020)

Mathematica Bohemica

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The present study aimed to introduce $n$ -fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of $n$ -fold (positive) implicative IVRL-extended filters and $n$ -fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the $n$ -fold IVRL-extended filters, $n$ -fold (positive) implicative algebras, and the Gödel triangle algebra were discussed. ...

Balcar's theorem on supports

Lev Bukovský (2018)

Commentationes Mathematicae Universitatis Carolinae

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In A theorem on supports in the theory of semisets [Comment. Math. Univ. Carolinae 14 (1973), no. 1, 1–6] B. Balcar showed that if $σ \subseteq D \in M$ is a support, $M$ being an inner model of ZFC, and $𝒫 (D ∖ σ) \cap M = r ` ` σ$ with $r \in M$ , then $r$ determines a preorder " $⪯$ " of $D$ such that $σ$ becomes a filter on $(D, ⪯)$ generic over $M$ . We show that if the relation $r$ is replaced by a function $𝒫 (D ∖ σ) \cap M = f_{- 1} (σ)$ , then there exists an equivalence relation " $\sim$ " on $D$ and a partial order on $D / \sim$ such that $D / \sim$ is a complete Boolean algebra, $σ / \sim$ is a generic filter and ${[f (u)]}_{\sim} = - \sum (u / \sim)$ for...

Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice

Lifeng Li, Jianke Zhang, Chang Zhou (2019)

Kybernetika

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For a t-norm T on a bounded lattice $(L, \leq)$ , a partial order $\leq_{T}$ was recently defined and studied. In [11], it was pointed out that the binary relation $\leq_{T}$ is a partial order on $L$ , but $(L, \leq_{T})$ may not be a lattice in general. In this paper, several sufficient conditions under which $(L, \leq_{T})$ is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on $L$ such that $(L, \leq_{T})$ is a lattice are presented.

Construction of uninorms on bounded lattices

Gül Deniz Çaylı, Funda Karaçal (2017)

Kybernetika

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In this paper, we propose the general methods, yielding uninorms on the bounded lattice $(L, \leq, 0, 1)$ , with some additional constraints on $e \in L ∖ {0, 1}$ for a fixed neutral element $e \in L ∖ {0, 1}$ based on underlying an arbitrary triangular norm $T_{e}$ on $[0, e]$ and an arbitrary triangular conorm $S_{e}$ on $[e, 1]$ . And, some illustrative examples are added for clarity.

$P_{λ}$ -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.

Orthogonality and complementation in the lattice of subspaces of a finite vector space

Ivan Chajda, Helmut Länger (2022)

Mathematica Bohemica

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We investigate the lattice $𝐋 (𝐕)$ of subspaces of an $m$ -dimensional vector space $𝐕$ over a finite field $GF (q)$ with a prime power $q = p^{n}$ together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice $𝐋 (𝐕)$ satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when $𝐋 (𝐕)$ is orthomodular....

On preimages of ultrafilters in ZF

Horst Herrlich, Paul Howard, Kyriakos Keremedis (2016)

Commentationes Mathematicae Universitatis Carolinae

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We show that given infinite sets $X, Y$ and a function $f : X \to Y$ which is onto and $n$ -to-one for some $n \in ℕ$ , the preimage of any ultrafilter $ℱ$ of $Y$ under $f$ extends to an ultrafilter. We prove that the latter result is, in some sense, the best possible by constructing a permutation model $ℳ$ with a set of atoms $A$ and a finite-to-one onto function $f : A \to ω$ such that for each free ultrafilter of $ω$ its preimage under $f$ does not extend to an ultrafilter. In addition, we show that in $ℳ$ there exists an ultrafilter compact...

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...

On the mappings $𝒵_{A}$ and $ℑ_{A}$ in intermediate rings of $C (X)$

Mehdi Parsinia (2018)

Commentationes Mathematicae Universitatis Carolinae

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In this article, we investigate new topological descriptions for two well-known mappings $𝒵_{A}$ and $ℑ_{A}$ defined on intermediate rings $A (X)$ of $C (X)$ . Using this, coincidence of each two classes of $z$ -ideals, $𝒵_{A}$ -ideals and $ℑ_{A}$ -ideals of $A (X)$ is studied. Moreover, we answer five questions concerning the mapping $ℑ_{A}$ raised in [J. Sack, S. Watson, $C$ and $C^{*}$ among intermediate rings, Topology Proc. 43 (2014), 69–82].

Explicit construction of normal lattice configurations

Mordechay B. Levin, Meir Smorodinsky (2005)

Colloquium Mathematicae

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We extend Champernowne’s construction of normal numbers to base b to the $ℤ^{d}$ case and obtain an explicit construction of a generic point of the $ℤ^{d}$ shift transformation of the set ${0, 1, . . ., b - 1}^{ℤ^{d}}$ .

Coherent ultrafilters and nonhomogeneity

Jan Starý (2015)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the notion of a coherent $P$ -ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a $P$ -point on $ω$ , and show that these ultrafilters exist generically under $𝔠 = 𝔡$ . This improves the known existence result of Ketonen [On the existence of $P$ -points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1,...