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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 5, Pages 1111–1132 (Mi smj2334)  
This article is cited in 9 scientific papers (total in 9 papers)

Lattices of subclasses

M. V. Semenovaab, A. Zamojska-Dzienioc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
c Warsaw University of Technology, Warsaw, Poland
Full-text PDF (395 kB) Citations (9)
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Abstract: We investigate the structure of lattices of subclasses of different types; among those are relative sub(quasi)variety lattices as well as relative (finitary) subprevariety lattices. Among other results, we prove a reduction theorem for (finitary) subprevariety lattices which generalizes a result of V. A. Gorbunov. We also answer a question by D. E. Palchunov and provide some noncomputability properties of lattices of relative subclasses.
Keywords: axiomatizable class, variety, quasivariety, prevariety, identity, quasi-identity, latticeю.
Received: 02.04.2011
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 5, Pages 889–905
DOI: https://doi.org/10.1134/S003744661205014X
Bibliographic databases:
Document Type: Article
UDC: 512.56+512.57+510.53
Language: Russian
Citation: M. V. Semenova, A. Zamojska-Dzienio, “Lattices of subclasses”, Sibirsk. Mat. Zh., 53:5 (2012), 1111–1132; Siberian Math. J., 53:5 (2012), 889–905
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/smj/v53/i5/p1111
    Cycle of papers
    This publication is cited in the following 9 articles:
    1. A. V. Kravchenko, M. V. Schwidefsky, “On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras”, Sib. elektron. matem. izv., 17 (2020), 753–768  mathnet  crossref
    2. Kravchenko A.V., Nurakunov A.M., Schwidefsky M.V., “on the Complexity of the Lattices of Subvarieties and Congruences”, Int. J. Algebr. Comput., 30:8 (2020), 1609–1624  crossref  mathscinet  zmath  isi  scopus
    3. Kravchenko A.V., Nurakunov A.M., Schwidefsky M.V., “on Representation of Finite Lattices”, Algebr. Universalis, 80:1 (2019), UNSP 15  crossref  mathscinet  isi  scopus
    4. S. M. Lutsak, “O slozhnosti reshetok kvazimnogoobrazii”, Sib. elektron. matem. izv., 14 (2017), 92–97  mathnet  crossref
    5. A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. elektron. matem. izv., 14 (2017), 252–263  mathnet  crossref
    6. M. V. Schwidefsky, “Complexity of quasivariety lattices”, Algebra and Logic, 54:3 (2015), 245–257  mathnet  crossref  crossref  mathscinet  isi
    7. A. M. Nurakunov, “Quasivariety lattices of pointed Abelian groups”, Algebra and Logic, 53:3 (2014), 238–257  mathnet  crossref  mathscinet  isi
    8. Schwidefsky M., Zamojska-Dzienio A., “Lattices of Subclasses. II”, Int. J. Algebr. Comput., 24:8 (2014), 1099–1126  crossref  mathscinet  zmath  isi  elib  scopus
    9. A. Nurakunov, M. Semenova, A. Zamojska-Dzienio, “On lattices connected with various types of classes of algebraic structures”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 167–179  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
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