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Wyświetlanie 1-15 z 40
Tytuł:
Classification systems and their lattice
Autorzy:
Radeleczki, Sándor
Powiązania:
https://bibliotekanauki.pl/articles/729009.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
concept lattice
CJ-generated complete lattice
atomistic complete lattice
(independent) classification system
classification lattice
box lattice
Opis:
We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent and Cls(L) is a partition lattice.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 2; 167-181
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On duality of submodule lattices
Autorzy:
Czédli, Gábor
Takách, Géza
Powiązania:
https://bibliotekanauki.pl/articles/728870.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
submodule lattice
lattice identity
duality
Opis:
An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 43-49
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some finite groupoids with distributive subgroupoid lattices
Autorzy:
Pióro, Konrad
Powiązania:
https://bibliotekanauki.pl/articles/729063.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
groupoid
subgroupoid lattice
distributive lattice
Opis:
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).
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 1; 25-31
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Quasiorder lattices are five-generated
Autorzy:
Kulin, Júlia
Powiązania:
https://bibliotekanauki.pl/articles/728856.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
quasiorder lattice
preorder lattice
accessible cardinal
Opis:
A quasiorder (relation), also known as a preorder, is a reflexive and transitive relation. The quasiorders on a set A form a complete lattice with respect to set inclusion. Assume that A is a set such that there is no inaccessible cardinal less than or equal to |A|; note that in Kuratowski's model of ZFC, all sets A satisfy this assumption. Generalizing the 1996 result of Ivan Chajda and Gábor Czéedli, also Tamás Dolgos' recent achievement, we prove that in this case the lattice of quasiorders on A is five-generated, as a complete lattice.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2016, 36, 1; 59-70
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cardinalities of lattices of topologies of unars and some related topics
Autorzy:
Kartashova, Anna
Powiązania:
https://bibliotekanauki.pl/articles/728762.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
unar
lattice of topologies
lattice of congruences
Opis:
In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 129-137
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite orders and their minimal strict completion lattices
Autorzy:
Bordalo, Gabriela
Monjardet, Bernard
Powiązania:
https://bibliotekanauki.pl/articles/728964.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
atomistic lattice
join-irreducible element
distributive lattice
modular lattice
lower semimodular lattice
Dedekind-MacNeille completion
strict completion
weak order.
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 85-100
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Distributivity of bounded lattices with sectionally antitone involutions
Autorzy:
Chajda, Ivan
Powiązania:
https://bibliotekanauki.pl/articles/729093.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
sectionally antitone involution
bounded lattice
distributive lattice
MV-algebra
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 2; 155-163
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On lattice-ordered monoids
Autorzy:
Jasem, Milan
Powiązania:
https://bibliotekanauki.pl/articles/728966.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
lattice-ordered monoid
normal lattice-ordered monoid
dually residuated lattice-ordered semigroup
direct decomposition
polar
Opis:
In the paper lattice-ordered monoids and specially normal lattice-ordered monoids which are a generalization of dually residuated lattice-ordered semigroups are investigated. Normal lattice-ordered monoids are metricless normal lattice-ordered autometrized algebras. It is proved that in any lattice-ordered monoid A, a ∈ A and na ≥ 0 for some positive integer n imply a ≥ 0. A necessary and sufficient condition is found for a lattice-ordered monoid A, such that the set I of all invertible elements of A is a convex subset of A and A¯ ⊆ I, to be the direct product of the lattice-ordered group I and a lattice-ordered semigroup P with the least element 0.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 101-114
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Balanced d-lattices are complemented
Autorzy:
Goldstern, Martin
Ploščica, Miroslav
Powiązania:
https://bibliotekanauki.pl/articles/729051.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
balanced congruence
balanced lattice
d-lattice
prime ideal
maximal ideal
Opis:
We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 1; 33-37
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Congruences on pseudocomplemented semilattices
Autorzy:
Heleyová, Zuzana
Powiązania:
https://bibliotekanauki.pl/articles/728824.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
pseudocomplemented semilattice
congruence lattice
p-algebra
Stone algebra
(relative) (Lₙ)-lattice
Opis:
It is known that congruence lattices of pseudocomplemented semilattices are pseudocomplemented [4]. Many interesting properties of congruences on pseudocomplemented semilattices were described by Sankappanavar in [4], [5], [6]. Except for other results he described congruence distributive pseudocomplemented semilattices [6] and he characterized pseudocomplemented semilattices whose congruence lattices are Stone, i.e. belong to the variety B₁ [5].
In this paper we give a partial solution to a more general question: Under what condition on a pseudocomplemented semilattice its congruence lattice is element of the variety Bₙ (n ≥ 2)?
In the last section we widen the Sankappanavar's result to obtain the description of pseudocomplemented semilattices with relative Stone congruence lattices. A partial solution of the description of pseudocomplemented semilattices with relative (Lₙ)-congruence lattices (n ≥ 2) is also given.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 219-231
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Isomorphisms of direct products of lattice-ordered groups
Autorzy:
Jakubík, Ján
Powiązania:
https://bibliotekanauki.pl/articles/728908.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Lattice-ordered group
direct product
Specker lattice-ordered group
orthogonal σ-completeness
Opis:
In this paper we investigate sufficient conditions for the validity of certain implications concerning direct products of lattice-ordered groups.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 1; 43-52
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On interval decomposition lattices
Autorzy:
Foldes, Stephan
Radeleczki, Sándor
Powiązania:
https://bibliotekanauki.pl/articles/728916.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
interval
closure system
modular decomposition
semimodular lattice
partition lattice
strong set
lexicographic sum
Opis:
Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Lattice-theoretical properties of decompositions are explored, and connections with particular types of intervals are established.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 1; 95-114
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A reduction theorem for ring varieties whose subvariety lattice is distributive
Autorzy:
Volkov, Mikhail
Powiązania:
https://bibliotekanauki.pl/articles/729065.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
variety of rings
subvariety lattice
distributive lattice
torsion-bounded variety
Mal'tsev product
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2010, 30, 1; 119-132
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice
Autorzy:
Chajda, Ivan
Länger, Helmut
Powiązania:
https://bibliotekanauki.pl/articles/728776.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
bounded lattice
antitone involution
complemented element
Opis:
Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2008, 28, 2; 251-259
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On ideals of a skew lattice
Autorzy:
Costa, João Pita
Powiązania:
https://bibliotekanauki.pl/articles/728981.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
noncommutative lattice
skew lattice
band of semigroups
ideals
coset structure
Green's relations
skew Boolean algebras
Opis:
Ideals are one of the main topics of interest when it comes to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be derived, respectively, from the two concepts of order that arise in the context of skew lattices. The correspondence between the ideals of a skew lattice, derived from the preorder, and the ideals of its respective lattice image is clear. Though, skew ideals, derived from the partial order, seem to be closer to the specific nature of skew lattices. In this paper we review ideals in skew lattices and discuss the intersection of this with the study of the coset structure of a skew lattice.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2012, 32, 1; 5-21
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 40

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