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Algebra Logika, 2001, Volume 40, Number 6, Pages 685–697 (Mi al242)  

This article is cited in 6 scientific papers (total in 6 papers)

Decompositions in Complete Lattices

M. V. Semenova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We give descriptions of lattices that have (unique) irredundant decompositions and decompositions with the replacement property in a class of fully join semidistributive upper continuous lattices and in a class of upper and lower continuous lattices. In particular, it is stated that unique irredundant decompositions in the classes in question coincide with minimal.

Keywords: lattice, semidistributive upper lattice, upper continuous lattice, upper and lower continuous lattice, irredundant decomposition

Full text: PDF file (1233 kB)

English version:
Algebra and Logic, 2001, 40:6, 384–390

Bibliographic databases:

UDC: 512.56
Received: 14.04.2000

Citation: M. V. Semenova, “Decompositions in Complete Lattices”, Algebra Logika, 40:6 (2001), 685–697; Algebra and Logic, 40:6 (2001), 384–390

Citation in format AMSBIB
\Bibitem{Sem01}
\by M.~V.~Semenova
\paper Decompositions in Complete Lattices
\jour Algebra Logika
\yr 2001
\vol 40
\issue 6
\pages 685--697
\mathnet{http://mi.mathnet.ru/al242}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1918525}
\zmath{https://zbmath.org/?q=an:1011.06008}
\transl
\jour Algebra and Logic
\yr 2001
\vol 40
\issue 6
\pages 384--390
\crossref{https://doi.org/10.1023/A:1013703825890}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-24344504615}


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    This publication is cited in the following articles:
    1. Erne M., “Intervals in lattices of kappa-meet-closed subsets”, Order-A Journal on the Theory of Ordered Sets and Its Applications, 21:2 (2004), 137–153  mathscinet  zmath  isi
    2. Wang XuePing, Qu XiaoBing, “The complete principal divisor lattices”, Science China-Mathematics, 53:8 (2010), 2159–2172  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Sun F., Wang X.-p., Qu X.-b., “Minimal Join Decompositions and their Applications to Fuzzy Relation Equations Over Complete Brouwerian Lattices”, Inf. Sci., 224 (2013), 143–151  crossref  mathscinet  zmath  isi  scopus
    4. Erne M., Joshi V., “Ideals in Atomic Posets”, Discrete Math., 338:6 (2015), 954–971  crossref  mathscinet  zmath  isi  scopus
    5. M. V. Schwidefsky, “Decompositions in complete lattices. II. Replaceable irredundant decompositions”, Algebra and Logic, 56:3 (2017), 236–244  mathnet  crossref  crossref  mathscinet  isi
    6. M. V. Schwidefsky, “Decompositions in complete lattices III. Unique irredundant decompositions and convex geometries”, Algebra and Logic, 56:5 (2017), 409–424  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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