In this book for the first time authors describe and develop the new notion of MOD natural neutrosophic semirings using Z^I_n, C_I(Zn), _I, _I, _I and _I.
Several interesting properties about this structure is derived. Using these MOD natural neutrosophic semirings MOD natural
neutrosophic matrix semirings and MOD natural neutrosophic polynomial semirings and defined and described. Special elements of these structures are analysed. When MOD intervals [0, n) and MOD natural neutrosophic intervals [0, n) are used we see the MOD semirings do not in general satisfy the associative laws and the distributive laws leading to the definition of pseudo semirings of infinite order. These are also introduced in this book. We also define and develop MOD subset pseudo semiring and MOD subset natural neutrosophic pseudo semirings. This study is innovative and interesting by providing a large class of MOD pseudo semirings. Special elements in them are analysed.
Using these MOD subset matrix pseudo semirings and MOD subset polynomial pseudo semirings and developed.
They enjoy very many special features. Several problems are suggested and these notions will certainly attract semiring theorists.
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