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If R(I) is a neutrosophic ring, then every subset of R(I) has the form 𝑀 = 𝑃 + 𝑆𝐼, where P,S are subsets of the classical ring R. The objective of this paper is to determine the necessary and sufficient condition on classical subsets P and S which makes M an ideal in R(I). The main result is proving that every classical ideal in a neutrosophic ring must be an AH-ideal and determining the form of maximal and minimal ideals in R(I). Also, a similar discussion of the case of refined neutrosophic rings will be presented.