Neutrosophic Extended Triplet Set upgraded

Therefore, let E be a set, and x in E. Then neut'(x) should be in E such that: x*neut'(x) = neut'(x)*x = x, where neut'(x) can be the unitary element of law * on E. Therefore, the axioms of the Neutrosophic Extended Triplet

Loop on (E,*) are: 1) (E,*) is an Neutrosophic Extended Triplet Set, i.e. for any x in E, one has neut'(x) (which can be the unitary element too) in E, such that x*neut'(x) = neut'(x)*x = x, and anti'(x) in E such that: x*anti'(x) = anti'(x)*x = neut'(x). I used the notation anti’(x) to distinguish it from the previous papers’ anti(x). 2) The law * is well-defined and non-associative. It will be interesting to compare the Neutrosophic Extended

Triplet Group with the General Group, and the

Neutrosophic Extended Triplet Loop with the

Neutrosophic Triplet Loop.

Neutrosophic Extended Triplet Set upgraded

To Tèmítópé Gbóláhàn Jaíyéolá I agree with your observation that any group becomes automatically a Neutrosophic Extended Triplet Group if we consider that the classical neutral element should be allowed into the set of neutral of x, denoted as {neut(x)}.

But let’s upgrade the definition of Neutrosophic Extended

Triplet Set as follow: 1) A set (E, *), with a well-defined law, such that there exist at least an element x in E that has 2 or more distinct neut(x)'s - where the classical neutral element with respect to the law * is allowed to belong to the set of neutrals {neut(y)}, for any y in E. We used { } to denote a set. In this case, not all classical groups are Neutrosophic

Extended Triplet Groups. 2) A set (E, *), with a well-defined law, such that there exist at least an element x in E that has 2 or more distinct anti(x)'s - where the classical neutral element with respect to the law * is allowed to belong to the set of neutrals {neut(y)}, for any y in E, and the classical symmetric element x-1 with respect to the law * is allowed to belong to the set of opposites {anti(y)}, for any y in E. In this case, similarly, not all classical groups are

Neutrosophic Extended Triplet Groups. Tèmítópé Gbóláhàn Jaíyéolá The opposite is dependent on neutrality, but neutrality is not necessarily dependent on opposite (generally speaking).