Abstract

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

Keywords: Fuzzy coprimary submodules; fuzzy coprimary representation; fuzzy attached primes.

MSC: 08A72

Pages:  201$-$211     

Volume  67 ,  Issue  3 ,  2015