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Abstract. This paper is a continuation for the study of the zero-divisor graph for the ring of Gaussian integers modulo n, ‫ޚ(‬ n [i] Let n be a natural number and let < n > be the principal ideal generated by n in ‫ [ޚ‬i]. Then the factor ring

LetEnbe the ring of Eisenstein integers modulon. In this paper we study the zero divisor graphΓ(En). We find the diameters and girths for such zero divisor graphs and characterizenfor which the graphΓ(En)is complete, complete bipartite, bipartite, regular, Eulerian, Hamiltonian, or chordal.

Let R be a commutative ring with unity. The main objective of this article is to study the relationships between PP-rings, generalized morphic rings and EM-rings. Although PP-rings are included in the later rings, the converse is not in general true. We put necessary and sufficient conditions to ensure the converse using idealization and polynomial rings