Paul, Isaac; Dr.Chakravarti, R S; Thrivikraman,T(Cochin University of Science and Technology, November , 2004)
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Abstract:
The
main objective of this thesis was to extend some basic concepts and results in
module theory in algebra to the fuzzy setting.The concepts like simple module, semisimple module and exact sequences
of R-modules form an important area of study in crisp module theory. In this
thesis generalising these concepts to the fuzzy setting we have introduced
concepts of ‘simple and semisimple L-modules’ and proved some results which
include results analogous to those in crisp case. Also we have defined and
studied the concept of ‘exact sequences of L-modules’.Further extending the concepts in crisp theory, we have introduced the
fuzzy analogues ‘projective and injective L-modules’. We have proved many
results in this context. Further we have defined and explored notion of ‘essential
L-submodules of an L-module’. Still there are results in crisp theory related to the
topics covered in this thesis which are to be investigated in the fuzzy setting.
There are a lot of ideas still left in algebra, related to the theory of
modules, such as the ‘injective hull of a module’, ‘tensor product of modules’
etc. for which the fuzzy analogues are not defined and explored.
Description:
Department of Mathematics, Cochin University of Science and Technology