On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings

This paper is a continuation of ideas presented by Davvaz [Roughness in rings, Inform. Sci., 164 (2004) 147–163; Roughness based on fuzzy ideals, Inform. Sci., 176 (2006) 2417–2437]. We introduce the notions of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in a ring, and give some properties of such ideals. Also, we discuss the relations between the upper and lower rough prime (primary) ideals and the upper and lower approximations of their homomorphism images.