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Sibirsk. Mat. Zh., 2012, Volume 53, Number 5, Pages 1111–1132 (Mi smj2334)  

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

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

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English version:
Siberian Mathematical Journal, 2012, 53:5, 889–905

Bibliographic databases:

UDC: 512.56+512.57+510.53
Received: 02.04.2011

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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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. 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
    2. A. M. Nurakunov, “Quasivariety lattices of pointed Abelian groups”, Algebra and Logic, 53:3 (2014), 238–257  mathnet  crossref  mathscinet  isi
    3. Schwidefsky M., Zamojska-Dzienio A., “Lattices of Subclasses. II”, Int. J. Algebr. Comput., 24:8 (2014), 1099–1126  crossref  mathscinet  zmath  isi  elib  scopus
    4. M. V. Schwidefsky, “Complexity of quasivariety lattices”, Algebra and Logic, 54:3 (2015), 245–257  mathnet  crossref  crossref  mathscinet  isi
    5. S. M. Lutsak, “O slozhnosti reshetok kvazimnogoobrazii”, Sib. elektron. matem. izv., 14 (2017), 92–97  mathnet  crossref
    6. A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. elektron. matem. izv., 14 (2017), 252–263  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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