Results 1 to 10 of about 243 (99)
Complete Congruence Lattices of Complete Distributive Lattices [PDF]
Journal of Algebra, 1995 The authors deal with the question of whether every complete lattice \(L\) is isomorphic to the lattice of complete congruence relations of a suitable complete lattice \(K\). They prove that \(K\) can always be chosen as a complete distributive lattice. In fact, they prove a more general result: Let \(m\) be a regular cardinal \(>\aleph_ 0\). Every \(m\
Gratzer, G., Schmidt, E.T.
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On L-fuzzy ideals of multilattices [PDF]
Journal of Hyperstructures, 2023 For a given multilattice M, the set ℑM of all ideals of M is a complete lattice and for a given complete lattice L, the set FI(M;L) of all L-fuzzy ideals ofMis also a complete lattice.
Daquin Cdric Awouafack +2 more
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On complete congruence lattices of complete lattices [PDF]
Transactions of the American Mathematical Society, 1991 The lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In this paper, we characterize this lattice as a complete lattice. In other words, for a complete latticeLL, we construct a complete latticeKKsuch thatLLis isomorphic to the lattice of complete congruence relations ofKK.
Grätzer, G., Lakser, H.
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The lattice of (2, 1)-congruences on a left restriction semigroup
Open Mathematics, 2022 All the (2, 1)-congruences on a left restriction semigroup become a complete sublattice of its lattice of congruences. The aim of this article is to study certain fundamental properties of this complete sublattice.
Liu Haijun, Guo Xiaojiang
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Completely representable lattices [PDF]
Algebra universalis, 2012 It is known that a lattice is representable as a ring of sets iff the lattice is distributive. CRL is the class of bounded distributive lattices (DLs) which have representations preserving arbitrary joins and meets. jCRL is the class of DLs which have representations preserving arbitrary joins, mCRL is the class of DLs which have representations ...
Egrot, R, Hirsch, R
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“Complete-simple” distributive lattices [PDF]
Proceedings of the American Mathematical Society, 1993 It is well known that the only simple distributive lattice is the two-element chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences. In this paper we show the existence of infinite complete-simple distributive lattices.
Grätzer, G., Schmidt, E. T.
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A relational semantics for the logic of bounded lattices [PDF]
Mathematica Bohemica, 2019 This paper aims to propose a complete relational semantics for the so-called logic of bounded lattices, and prove a completeness theorem with regard to a class of two-sorted frames that is dually equivalent (categorically) to the variety of bounded ...
Luciano J. González
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Fuzzy Results for Finitely Supported Structures
Mathematics, 2021 We present a survey of some results published recently by the authors regarding the fuzzy aspects of finitely supported structures. Considering the notion of finite support, we introduce a new degree of membership association between a crisp set and a ...
Andrei Alexandru, Gabriel Ciobanu
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S-Implications on Complete Lattices and the Interval Constructor
Trends in Computational and Applied Mathematics, 2008 The aim of this work is to present an approach of interval fuzzy logic based on complete lattices. In particular, we study the extensions of the notions of t-conorms, fuzzy negations and S-implication, from the unit interval to arbitrary complete ...
R.H.S. Reiser +4 more
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ON COMPLETE CONGRUENCE LATTICES OF COMPLETE MODULAR LATTICES [PDF]
International Journal of Algebra and Computation, 1991 The lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In 1988, the second author announced the converse: every complete lattice L can be represented as the lattice of complete congruence relations of some complete lattice K.
R. FREESE, G. GRÄTZE, E. T. SCHMIDT
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