Abstract
In this paper we present the generalization of neutrosophic rings and neutrosophic fields. We also ex- tend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of no- tions which are related to the strong or pure part of neu- trosophy. We have given sufficient amount of examples to illustrate the theory of neutrosophic birings, neutro- sophic N-rings with neutrosophic bifields and neutro- sophic N-fields and display many properties of them in this paper.
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