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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2019, том 27, выпуск 1, страницы 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

Аннотация: 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).

Ключевые слова: quasivarieties, lattices, modules, Dedekind rings.

MSC: 08A62, 08C15, 20N02, 20N05

Поступила в редакцию: 22.06.2017
Исправленный вариант: 12.09.2017

Язык публикации: английский



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