In this paper, we study homomorphic images of interval valued L-fuzzy ideals of a nearring. If f : N 1 → N 2 is an onto nearring homomorphism andμ is an interval valued L-fuzzy ideal of N 2 then we prove that f −1 (μ) is an interval valued L-fuzzy ideal of N 1 . If μ is an interval valued L-fuzzy ideal of N 1 then we show that f (μ) is an interval valued Lfuzzy ideal of N 2 wheneverμ is invariant under f and interval valued t-norm is idempotent. Finally, we define interval valued L-fuzzy cosets and prove isomorphism theorems.

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In this chapter, for an ideal I of 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 G I (N). We prove that diam(EQ I (N \ I)) ≤ 3 and diam(C I (N \ I)) ≤ 3 and show 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.