Fuzzy representable modules and fuzzy attached primes

Abstract

Let $M$ be a non-zero unitary module over a non-zero commutative ring $R$. A kindof uniqueness theorem for a non-zero fuzzy representable submodule$\mu$ of $M$ will be proved, and then the set of fuzzy attachedprimes of $\mu$ will be defined. Then among other things, it will beshown that, whenever $R$ is Noetherian, a fuzzy prime ideal $\xi$ isattached to $\mu$ if and only if $\xi$ is the annihilator of a fuzzyquotient of $\mu$. The behavior of fuzzy attached primes with fuzzyquotient and fuzzy localization techniques will be studied.