International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 5, Pages 747-754
doi:10.1155/IJMMS.2005.747
On injective L-modules
Department of Mathematics, Bharata Mata College, Thrikkakara, Kochi 682 021, Kerala, India
Received 30 June 2004; Revised 18 November 2004
Copyright © 2005 Paul Isaac. 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 0→μ→fv→gη→0 is a short exact sequence of L-modules, then ν≃μ⊕η.