Neutrosophic Triplet as extension of Matter Plasma, Unmatter Plasma, and Antimatter Plasma

A Neutrosophic Triplet, is a triplet of the form: <a, neut(a), and anti(a) >, where neut(a) is the neutral of a, i.e. an element (different from the identity element of the operation *) such that a*neut(a) = neut(a)*a = a, while anti(a) is the opposite of a, i.e. an element such that a*anti(a) = anti(a)*a = neut(a). Neutrosophy means not only indeterminacy, but also neutral (i.e. neither true nor false). For example we can have neutrosophic triplet semigroups, neutrosophic triplet loops, etc. As a particular case of the Neutrosophic Triple, in physics one has <Matter, Unmatter, Antimatter>and its corresponding triplet <Matter Plasma, Unmatter Plasma, Antimatter Plasma>. We further extended it to an m-valued refined neutrosophic triplet, in a similar way as it was done for T₁, T₂, ...; I₁, I₂, ...; F₁, F₂, ... (i.e. the refinement of neutrosophic components). We may have a neutrosophic m-tuple with respect to the element ``a'' in the following way: (a; neut₁(a), neut₂(a), ..., neut_p(a); anti₁(a), anti₂(a), ..., anti_p(a)), where m = 1 +2p, such that: - all neut₁(a), neut₂(a), ..., neut_p(a) are distinct two by two, and each one is different from the unitary element with respect to the composition law *; - also a*neut₁(a) = neut₁(a)*a = a, a*neut₂(a) = neut₂(a)*a = a, ..., a*neut_p(a) = neut_p(a)*a = a; - and a*anti₁(a) = anti₁(a)*a = neut₁(a), a*anti₂(a) = anti₂(a)*a = neut2(a), ..., a*anti_p(a) = anti_p(a)*a = neut_p(a); - where all anti₁(a), anti₂(a), ..., anti_p(a) are distinct two by two, and in case when there are duplicates, the duplicates are discarded.