ON PROJECTIVE L- MODULES

Document Type: Research Paper

Author

DEPARTMENT OF MATHEMATICS, BHARATA MATA COLLEGE, THRIKKAKARA KOCHI - 682 021, KERALA, INDIA

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 projective L-modules. We prove that every free L-module is a
projective L-module. Also we prove that if μ∈L(P) is a projective L-module, and if
0→η f→ ν g→ μ →0 is a short exact sequence of L-modules then η⊕ μ >ν.
Further it is proved that if μ∈L(P) is a projective L-module then μ is a fuzzy direct summand
of a free L-module.

Keywords


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