Generalized $P_0$-lattices of order ω+

T. Traczyk; W. Zarębski

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Displaying similar documents to “Generalized $P_{0}$ -lattices of order ω+”

Generalized $P_{1}$ - and $P_{2}$ -lattices of order ω+

W. Zarębski (1977)

Colloquium Mathematicae

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A new approach to construct uninorms via uninorms on bounded lattices

Zhen-Yu Xiu, Xu Zheng (2024)

Kybernetika

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In this paper, on a bounded lattice $L$ , we give a new approach to construct uninorms via a given uninorm $U^{*}$ on the subinterval $[0, a]$ (or $[b, 1]$ ) of $L$ under additional constraint conditions on $L$ and $U^{*}$ . This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.

Configurations of rank- $40 r$ extremal even unimodular lattices ( $r = 1, 2, 3$ )

Scott Duke Kominers, Zachary Abel (2008)

Journal de Théorie des Nombres de Bordeaux

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We show that if $L$ is an extremal even unimodular lattice of rank $40 r$ with $r = 1, 2, 3$ , then $L$ is generated by its vectors of norms $4 r$ and $4 r + 2$ . Our result is an extension of Ozeki’s result for the case $r = 1$ .

Differentiation and splitting for lattices over orders

Wolfgang Rump (2001)

Colloquium Mathematicae

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We extend our module-theoretic approach to Zavadskiĭ’s differentiation techniques in representation theory. Let R be a complete discrete valuation domain with quotient field K, and Λ an R-order in a finite-dimensional K-algebra. For a hereditary monomorphism u: P ↪ I of Λ-lattices we have an equivalence of quotient categories $\partial ̃_{u} : Λ - l a t / [ℋ] ⭇ δ_{u} Λ - l a t / [B]$ which generalizes Zavadskiĭ’s algorithms for posets and tiled orders, and Simson’s reduction algorithm for vector space categories. In this article we replace...

A class of multiplicative lattices

Tiberiu Dumitrescu, Mihai Epure (2021)

Czechoslovak Mathematical Journal

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We study the multiplicative lattices $L$ which satisfy the condition $a = (a : (a : b)) (a : b)$ for all $a, b \in L$ . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group $ℤ$ or $ℝ$ . A sharp lattice $L$ localized at its maximal elements are totally ordered sharp lattices. The converse is true if $L$ has finite character.

Modular lattices from finite projective planes

Tathagata Basak (2014)

Journal de Théorie des Nombres de Bordeaux

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Using the geometry of the projective plane over the finite field $𝔽_{q}$ , we construct a Hermitian Lorentzian lattice $L_{q}$ of dimension $(q^{2} + q + 2)$ defined over a certain number ring $𝒪$ that depends on $q$ . We show that infinitely many of these lattices are $p$ -modular, that is, $p L_{q}^{'} = L_{q}$ , where $p$ is some prime in $𝒪$ such that ${| p |}^{2} = q$ . The Lorentzian lattices $L_{q}$ sometimes lead to construction of interesting positive definite lattices. In particular, if $q \equiv 3 mod 4$ is a rational prime such that $(q^{2} + q + 1)$ is norm of some element in...

The extension of the Krein-Šmulian theorem for order-continuous Banach lattices

Antonio S. Granero, Marcos Sánchez (2008)

Banach Center Publications

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If X is a Banach space and C ⊂ X a convex subset, for x** ∈ X** and A ⊂ X** let d(x**,C) = inf||x**-x||: x ∈ C be the distance from x** to C and d̂(A,C) = supd(a,C): a ∈ A. Among other things, we prove that if X is an order-continuous Banach lattice and K is a w*-compact subset of X** we have: (i) $d ̂ ({\bar{c o}}^{w *} (K), X) \leq 2 d ̂ (K, X)$ and, if K ∩ X is w*-dense in K, then $d ̂ ({\bar{c o}}^{w *} (K), X) = d ̂ (K, X)$ ; (ii) if X fails to have a copy of ℓ₁(ℵ₁), then $d ̂ ({\bar{c o}}^{w *} (K), X) = d ̂ (K, X)$ ; (iii) if X has a 1-symmetric basis, then $d ̂ ({\bar{c o}}^{w *} (K), X) = d ̂ (K, X)$ .

Structural aspects of truncated archimedean vector lattices: good sequences, simple elements

Richard N. Ball (2021)

Commentationes Mathematicae Universitatis Carolinae

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The truncation operation facilitates the articulation and analysis of several aspects of the structure of archimedean vector lattices; we investigate two such aspects in this article. We refer to archimedean vector lattices equipped with a truncation as truncs. In the first part of the article we review the basic definitions, state the (pointed) Yosida representation theorem for truncs, and then prove a representation theorem which subsumes and extends the (pointfree) Madden representation...

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.

On the structural theory of ${II}_{1}$ factors of negatively curved groups

Ionut Chifan, Thomas Sinclair (2013)

Annales scientifiques de l'École Normale Supérieure

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Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor $L Γ$ is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that $L Γ$ is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in $Sp (n, 1)$ , $n \geq 2$ , are virtually $W^{*}$ -superrigid.

$G$ -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.

The existence of $P (α)$ -points of N* for $ℵ_{0} α < 𝔠$

A. Szymański (1977)

Colloquium Mathematicae

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On C $^{*}$ -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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On a characterization of $L^{p}$ -norm

Janusz Matkowski (1989)

Annales Polonici Mathematici

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$ℵ_{1}$ -incompactness of Z

Ralph McKenzie (1971)

Colloquium Mathematicae

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Displaying similar documents to “Generalized P 0 -lattices of order ω+”

Displaying similar documents to “Generalized $P_{0}$ -lattices of order ω+”