Kandasamy and Smarandache [7] introduced the philosophical

algebraic structures, in particular, Neutrosophic

algebraic structures with illustrations and examples in 2006 and initiated the new way for the emergence of a new class of structures, namely, Neutrosophic groupoids, Neutrosophic groups, Neutrosophic rings etc.

Connections should be made between different contexts where the same

algebraic structures arise.

They stress the importance of learning activities that assist students to recognise and use numerical structures that can be easily translated for understanding of

algebraic structures at a later time.

In his paper he also discussed certain

algebraic structures called triplexes.

The notion of neutrosophic

algebraic structures was introduced by Kandasamy and Smarandache in 2006, see [12, 13].

3] Florentin Smarandache, Special

algebraic structures, University of Maxico, Craiova, 1973.

They write for mathematicians, physicists, and computer scientists interested in theoretical relationships between graph theory,

algebraic structures, and physics.

The notion of a combinatorial Hopf algebra is a heuristic one, referring to rich

algebraic structures arising naturally on the linear spans of various families of combinatorial objects.

Since the structure is non-assosiative, but it has close relations with other

algebraic structures like semigroup and commutative structures.

The classification of such

algebraic structures was performed in [43].

This note contributes to the search for what are often large

algebraic structures (infinite dimensional spaces, infinitely generated algebras, among others) of functions on R or C having certain pathological properties.

Cohen); Birational aspects of the geometry of Mg(Gavril Farkas); The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces (Samuel Grushevsky and Igor Krichever); Brill-Noether theory (Joe Harris); GL+2(R)-orbit closures via topological splittings (Pascal Hubert, Erwan Lanneau, and Martin Moller); Harmonic mappings and moduli spaces of Riemann surfaces (Jurgen Jost and Shing Tung Yau);

Algebraic structures on the topology of moduli spaces of curves and maps (Y.