International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 980320, 12 pages
http://dx.doi.org/10.1155/2011/980320
Research Article

Fuzzy Small Submodule and Jacobson 𝐿 -Radical

Saifur Rahman1 and Helen K. Saikia2

1Department of Mathematics, Rajiv Gandhi University, Itanagar 791112, India
2Department of Mathematics, Gauhati University, Guwahati 781014, India

Received 22 December 2010; Accepted 2 March 2011

Academic Editor: Enrico Obrecht

Copyright © 2011 Saifur Rahman and Helen K. Saikia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.