In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields. We also extend neutrosophic ideal theory to form soft neutrosophic ideal over a neutrosophic ring and soft neutrosophic ideal of a soft neutrosophic ring . We have given many examples to illustrate the theory of soft neutrosophic rings and soft neutrosophic fields and display many properties of of these. At the end of this paper we (...) gave soft neutrosophic ring homomorphism. (shrink)

In this paper we extend the neutrosophic group and subgroup to soft neutrosophic group and soft neutrosophic subgroup respectively. Properties and theorems related to them are proved and many examples are given.

In this paper we extend the theory of neutrosophy to study left almost semigroup shortly LAsemigroup. We generalize the concepts of LA-semigroup to form that for neutrosophic LA-semigroup. We also extend the ideal theory of LA-semigroup to neutrosophy and discuss different kinds of neutrosophic ideals. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given many examples to illustrate the theory of neutrosophic LA-semigroup and display many properties (...) of neutrosophic LA-semigroup in this paper. (shrink)

In this paper we define neutrosophic bi-LAsemigroup and neutrosophic N-LA-semigroup. Infact this paper is an extension of our previous paper neutrosophic left almost semigroup shortly neutrosophic LAsemigroup. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given sufficient amount of examples to illustrate the theory of neutrosophic bi-LA-semigroup, neutrosophic N-LAsemigroup and display many properties of them (...) this paper. (shrink)

Soft neutrosophic group and soft neutrosophic subgroup are generalized to soft neutrosophic bigroup and soft neutrosophic N-group respectively in this paper. Different kinds of soft neutrosophic bigroup and soft neutrosophic N-group are given. The structural properties and theorems have been discussed with a lot of examples to disclose many aspects of this beautiful man made structure.