W. B. Vasantha Kandasamy, Florentin Smarandache
2016
In this book authors for the first time introduce the notion of MOD subsets. The S-semigroups enjoy several interesting properties. The notion of MOD universal subset and MOD absorbing subsets are defined and developed. MOD natural neutrosophic subsets forms only a semigroup under ‘+’. In fact the main feature enjoyed by this structure is they have subset idempotents with respect to ‘+’. They are S-semigroups under ‘+’. These MOD natural neutrosophic subsets of all 6 types are only semigroups under ‘x’. These enjoy distinct properties depending on the subset that is used. Further in these cases two types of products can be used one zero dominated product and the other MOD natural neutrosophic zero dominated product. Both the product are different. Finally using these MOD subsets matrices and polynomials are defined and developed. The new notion of MOD subset matrices are defined and these collections also under ‘+’ (or ‘x’) are only semigroups. On similar lines MOD subset polynomials are defined and they also form only a semigroup under ‘+’ (or ‘x’). These new notions are interesting and researchers can find lots of applications where semigroups find their applications. Several problems at research level are also suggested for the readers.
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