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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 5, Pages 747-754
http://dx.doi.org/10.1155/IJMMS.2005.747

On injective L-modules

Department of Mathematics, Bharata Mata College, Thrikkakara, Kochi, Kerala 682 021, India

Received 30 June 2004; Revised 18 November 2004

Copyright © 2005 Hindawi Publishing Corporation. 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

The concepts of free modules, projective modules, injective modules, and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper, we give an alternate definition for injective L-modules and prove that a direct sum of L-modules is injective if and only if each L-module in the sum is injective. Also we prove that if J is an injective module and μ is an injective L-submodule of J, and if 0μfvgη0 is a short exact sequence of L-modules, then νμη.