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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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A Note on some Characterization of Distributive Lattices of Finite Length

100%
Łazarz M., Siemieńczuk K., Department of Logic and Methodology of Sciences University of Wrocław P., lazarzmarcin@poczta.onet.pl, logika6@gmail.com
Bulletin of the Section of Logic
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2015
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tom 44
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nr 1-2
EN
Using known facts we give a simple characterization of the distributivity of lattices of finite length.
2
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Prime ideals in the lattice of additive induced-hereditary graph properties

80%
Berger A., Mihók P.
Discussiones Mathematicae Graph Theory
|
2003
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tom 23
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nr 1
117-127
EN
An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove that the prime ideals of the lattice of all additive induced-hereditary properties are divided into two groups, determined either by a set of excluded join-irreducible properties or determined by a set of excluded properties with infinite join-decomposability number. We provide non-trivial examples of each type.
3
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On some finite groupoids with distributive subgroupoid lattices

80%
Pióro K.
Discussiones Mathematicae - General Algebra and Applications
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2002
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tom 22
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nr 1
25-31
EN
The aim of the paper is to show that if S(G) is distributive, and also G satisfies some additional condition, then the union of any two subgroupoids of G is also a subgroupoid (intuitively, G has to be in some sense a unary algebra).
4
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Distributivity of bounded lattices with sectionally antitone involutions

80%
Chajda I.
Discussiones Mathematicae - General Algebra and Applications
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2005
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tom 25
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nr 2
155-163
EN
We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.
5
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Bounded lattices with antitone involutions and properties of MV-algebras

80%
Chajda I., Emanovský P.
Discussiones Mathematicae - General Algebra and Applications
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2004
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tom 24
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nr 1
31-42
EN
We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by L or A(L) to obtain all axioms of MV-algebra.
6
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Semiring of Sets

80%
Coghetto R.
Formalized Mathematics
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2014
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tom 22
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nr 1
79-84
EN
Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.
7
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A reduction theorem for ring varieties whose subvariety lattice is distributive

70%
Volkov M.
Discussiones Mathematicae - General Algebra and Applications
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2010
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tom 30
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nr 1
119-132
EN
We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.
8
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Distributive lattices with a given skeleton

61%
Grygiel J.
Discussiones Mathematicae - General Algebra and Applications
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2004
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tom 24
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nr 1
75-94
EN
We present a construction of finite distributive lattices with a given skeleton. In the case of an H-irreducible skeleton K the construction provides all finite distributive lattices based on K, in particular the minimal one.
9
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Finite orders and their minimal strict completion lattices

51%
Bordalo G., Monjardet B.
Discussiones Mathematicae - General Algebra and Applications
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2003
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tom 23
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nr 2
85-100
EN
Whereas the Dedekind-MacNeille completion D(P) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P)∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is join-irreducible). In this paper we study lattices which are minimal strict completions of finite orders. Such lattices are in one-to-one correspondence with finite posets. Among other results we show that, for every finite poset P, D(P)∗ is always generated by its doubly-irreducible elements. Furthermore, we characterize the posets P for which D(P)∗ is a lower semimodular lattice and, equivalently, a modular lattice.
10
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Power-ordered sets

51%
Goldstern M., Schweigert D.
Discussiones Mathematicae - General Algebra and Applications
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2002
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tom 22
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nr 1
39-46
EN
We define a natural ordering on the power set 𝔓(Q) of any finite partial order Q, and we characterize those partial orders Q for which 𝔓(Q) is a distributive lattice under that ordering.
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