Interval Groupoids

This book introduces several new classes of groupoid, like polynomial groupoids, matrix groupoids, interval groupoids,polynomial interval groupoids, matrix interval groupoids and their neutrosophic analogues. Interval groupoid happens to be the first non-associative structure constructed using intervals built using Zn or Z or Q or R or Z+ \cup {0} or Q+ \cup {0} and so on. This book has five chapters. Chapter one is introductory in nature. In chapter two new classes of groupoids and interval groupoids are defined and described. The analogous neutrosophic study is carried out in chapter three. The applications of this new structure is given in chapter four. The final chapter suggests more than 200 problems. This book has given 77 new definitions, 426 examples of these new notions and over 150 theorems.

💡 Research Summary

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The monograph “Interval Groupoids” introduces a broad new family of non‑associative algebraic structures built from intervals over familiar number systems such as the integers modulo n ( (Z_n) ), the integers (Z), the rationals (Q), the reals (R), and their non‑negative extensions. The central idea is to replace ordinary elements by closed intervals (