Fuzzy small submodule and Jacobson \(L\)-radical
type: Item
instance of: scholarly article
title: Fuzzy small submodule and Jacobson \(L\)-radical
zbMATH Open document ID: 1213.13030
DOI: 10.1155/2011/980320
author: Saifur Rahman
author: Helen K. Saikia
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-05-27T00:00:00Z
full work available at URL: https://eudml.org/doc/228323
review text: Summary: Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum. Fuzzy small submodules of a module are characterized in terms of fuzzy quotient modules. This characterization gives rise to some results on fuzzy coessential extensions. Finally, a relation between small \(L\)-submodules and Jacobson \(L\)-radical is established.
Mathematics Subject Classification ID: 13C99
zbMATH DE Number: 5900755
Wikidata QID: Q58688011
MaRDI profile type: Publication
OpenAlex ID: W1974284608
cites work: Fuzzy sets
cites work: Fuzzy groups
cites work: Fuzzy finitely generated modules
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description: scientific article; zbMATH DE number 5900755