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Algebra and Discrete Mathematics, 2004, Issue 1, Pages 75–86 (Mi adm329)  
This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

On lattices, modules and groups with many uniform elements

Jan Krempa

Institute of Mathematics Warsaw University ul. Banacha 2, 02–097 Warszawa POLAND
Full-text PDF (224 kB) Citations (1)
Abstract: The uniform dimension, also known as Goldie dimension, can be defined and used not only in the class of modules, but also in large classes of lattices and groups. For considering this dimension it is necessary to involve uniform elements.
In this paper we are going to discuss properties of lattices with many uniform elements. Further, we examine these properties in the case of lattices of submodules and of subgroups. We also formulate some questions related to the subject of this note.
Keywords: uniform element, locally uniform lattice, lattice of subgroups, lattice of submodules.
Received: 25.11.2003
Revised: 29.01.2004
Bibliographic databases:
Document Type: Article
MSC: 06C99, 16S90, 20E15
Language: English
Citation: Jan Krempa, “On lattices, modules and groups with many uniform elements”, Algebra Discrete Math., 2004, no. 1, 75–86
Citation in format AMSBIB
\Bibitem{Kre04}
\by Jan~Krempa
\paper On lattices, modules and groups with many uniform elements
\jour Algebra Discrete Math.
\yr 2004
\issue 1
\pages 75--86
\mathnet{http://mi.mathnet.ru/adm329}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2051382}
\zmath{https://zbmath.org/?q=an:1067.06005}
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  • https://www.mathnet.ru/eng/adm329
  • https://www.mathnet.ru/eng/adm/y2004/i1/p75
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Algebra and Discrete Mathematics
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