Study on Fuzzy Primes and Primary Submodules

Abstract

In this chapter the author attempts to fuzzify the concepts of prime, primary submodules and the radical of a fuzzy submodule. These concepts are studied in terms of their level submodules. Some properties of quotient of a fuzzy submodule and the intersection of two fuzzy primary submodules are discussed. The algebraic nature of fuzzy prime submodules and radical of fuzzy prime submodule is also carried out. Finally, fuzzy cosets of fuzzy submodules are also defined.