A common generalization of fuzzy primes

Naser Zamani, Zeinab Rezaei

Let $R$ be a commutative ring with identity. Let $FI(R)$ be the set of all fuzzy ideals of $R$ and $\phi:FI(R)\rightarrow FI(R)\cup\{0_R\}$ be a function. We introduce the concept of fuzzy $\phi$-prime ideals of $R$ and study some of its properties. It will be shown that under additional conditions fuzzy $\phi$-primeness implies fuzzy primeness. We also prove that in the decomposable rings fuzzy $\phi_{(1)}$-primes and fuzzy primes coincide. The behavior of this concept with fuzzy localization and fuzzy quotient is also studied.