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Neutrosophic Triplet Structures
By the way, you can define yourself the neutrosophic inverse starting with its axioms (or properties) that a neutrosophic inverse should accomplish: what / how do you expect that A-1 should behave in connection with A ? You said using logic; yes, it is a good idea.
Neutrosophic Triplet Structures
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To Kul Hur You gave examples in Zn in order to explain some concepts and results. It was the easiest example to make people understand the concept of "neutrosophic triplet" (NT). But of course many other examples can be done in broader form, I mean not only in the set of integers modulo n. Only one single paper was published in NT structures! It is very very new. Florentin Smarandache Then by starting a fixed semigroup "S", we want to define "neut(a) and anti(a)" for a member a ∊ S. It is a good idea. And in the above sense, we want to use "neutrosophic triplet subgroup" of a semigroup. Let (S, #) be a semigroup, so the law # is well-defined and associative.
If there exist neutrosophic triplets <a, neut(a), anti(a)>, for "a" in S, indeed their set, let's denote it by R, will form a neutrosophic triplet group, which is actually a neutrosophic triplet subgroup of S, as you said. Kul Hur Thus it is not necessary to define "neutrosophic commutative triplet group". Florentin Smarandache If the law # is not commutative, then the neutrosophic triplet (sub)group is not commutative either. If the law # is commutative, then the neutrosophic triplet (sub)group is commutative either. (R, #) may be a non-commutative neutrosophic triplet group, or a commutative neutrosophic triplet group, depending on # if non-commutative or commutative respectively on R. Kul Hur If you want to define "neutrosophic triplet group" and "neutrosophic commutative triplet group", then in order to do examples, it is not necessary to consider Zn. Florentin Smarandache Right, we need another type of algebraic structure (different from Zn), endowed with a law # which is not commutative. So, please do not identify the neutrosophic triplet set/subgroup/group etc. with Zn,
