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Algebra and Discrete Mathematics, 2019, Volume 27, Issue 1, Pages 37–49 (Mi adm690)  
RESEARCH ARTICLE

The lattice of quasivarietes of modules over a Dedekind ring

Přemysl Jedličkaa, Katarzyna Matczakb, Anna Mućkac

a Department o Mathematics, Faculty of Engineering, Czech University of Life Sciences, 165 21 Prague, Czech Republic
b Faculty of Civil Engineering, Mechanics and Petrochemistry in Płock, Warsaw University of Technology, 09-400 Płock, Poland
c Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland
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Abstract: In 1995 D. V. Belkin described the lattice of quasivarieties of modules over principal ideal domains [1]. The following paper provides a description of the lattice of subquasivarieties of the variety of modules over a given Dedekind ring. It also shows which subvarieties of these modules are deductive (a variety is deductive if every subquasivariety is a variety).
Keywords: quasivarieties, lattices, modules, Dedekind rings.
Funding agency Grant number
European Regional Development Fund 7AMB13PL013
8829/R13/R14
The joint research within the framework of the Polish–Czech cooperation grant no. 7AMB13PL013 and no. 8829/R13/R14.
Received: 22.06.2017
Revised: 12.09.2017
Document Type: Article
MSC: 08A62, 08C15, 20N02, 20N05
Language: English
Citation: Přemysl Jedlička, Katarzyna Matczak, Anna Mućka, “The lattice of quasivarietes of modules over a Dedekind ring”, Algebra Discrete Math., 27:1 (2019), 37–49
Citation in format AMSBIB
\Bibitem{JedMatMuc19}
\by Přemysl~Jedli{\v{c}}ka, Katarzyna Matczak, Anna Mu\'cka
\paper The lattice of quasivarietes of modules over a~Dedekind ring
\jour Algebra Discrete Math.
\yr 2019
\vol 27
\issue 1
\pages 37--49
\mathnet{http://mi.mathnet.ru/adm690}
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