Displaying similar documents to “Dieudonné-type theorems for lattice group-valued k -triangular set functions”

Hyperreflexivity of bilattices

Kamila Kliś-Garlicka (2016)

Czechoslovak Mathematical Journal

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The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice ℒ we can construct the bilattice Σ ℒ . Similarly, having a bilattice Σ we may consider the lattice ℒ Σ . In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples...

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 , ≤ ) , a partial order ≤ T was recently defined and studied. In [11], it was pointed out that the binary relation ≤ T is a partial order on L , but ( L , ≤ T ) may not be a lattice in general. In this paper, several sufficient conditions under which ( L , ≤ 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 , ≤ T ) is a lattice are presented.

On the special context of independent sets

Vladimír Slezák (2001)

Discussiones Mathematicae - General Algebra and Applications

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In this paper the context of independent sets J L p is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.

An extension method for t-norms on subintervals to t-norms on bounded lattices

Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu (2019)

Kybernetika

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In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on L from the t-norm on a subinterval of L need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other...

Some methods to obtain t-norms and t-conorms on bounded lattices

Gül Deniz Çaylı (2019)

Kybernetika

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In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice L based on a priori given t-norm acting on [ a , 1 ] and t-conorm acting on [ 0 , a ] for an arbitrary element a ∈ L ∖ { 0 , 1 } . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice. ...

Reducing the lengths of slim planar semimodular lattices without changing their congruence lattices

Gábor Czédli (2024)

Mathematica Bohemica

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Following G. Grätzer and E. Knapp (2007), a slim planar semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no M 3 as a sublattice. An SPS lattice is a slim rectangular lattice if it has exactly two doubly irreducible elements and these two elements are complements of each other. A finite poset P is said to be JConSPS-representable if there is an SPS lattice L such that P is isomorphic to the poset J ( Con L ) of join-irreducible congruences of L . We prove that...

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....

Generalized Schröder matrices arising from enumeration of lattice paths

Lin Yang, Sheng-Liang Yang, Tian-Xiao He (2020)

Czechoslovak Mathematical Journal

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We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps E = ( 1 , 0 ) , D = ( 1 , 1 ) , N = ( 0 , 1 ) , and D ' = ( 1 , 2 ) and not going above the line y = x . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest....

Lattice copies of c₀ and ℓ ∞ in spaces of integrable functions for a vector measure

S. Okada, W. J. Ricker, E. A. Sánchez Pérez

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The spaces L¹(m) of all m-integrable (resp. L ¹ w ( m ) of all scalarly m-integrable) functions for a vector measure m, taking values in a complex locally convex Hausdorff space X (briefly, lcHs), are themselves lcHs for the mean convergence topology. Additionally, L ¹ w ( m ) is always a complex vector lattice; this is not necessarily so for L¹(m). To identify precisely when L¹(m) is also a complex vector lattice is one of our central aims. Whenever X is sequentially complete, then this is the case. If,...

On central atoms of Archimedean atomic lattice effect algebras

Martin Kalina (2010)

Kybernetika

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If element z of a lattice effect algebra ( E , ⊕ , 0 , 1 ) is central, then the interval [ 0 , z ] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕ . It is a known fact that if the set C ( E ) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C ( E ) in E equals to the top element of E , then E is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether C ( E ) is...