Narrow Results

Let I be an ideal of a nearring N. We introduce the notions of equiprime graph of N denoted by EQ_I (N) and c-prime graph of N denoted by C_I (N). We relate EQ_I (N), C_I (N) and the graph of a nearring with respect to an ideal, G_I (N). We prove that diam(EQ_I (N\I)) ≤ 3 and diam(C_I (N\I)) ≤ 3 and deduce that the prime graphs are edge partitionable. It is well-known that the homomorphic image of a prime ideal need not be a prime ideal in general. We study graph homomorphisms and obtain conditions under which the primeness property of an ideal is preserved under nearring homomorphisms.