N-Algebraic Structures and S-N-Algebraic Structures

TL;DR

This paper introduces a new class of algebraic structures called N-algebraic structures, including N-groups, N-semigroups, N-loops, and N-groupoids, with numerous definitions and potential applications in automata, coloring, and coding theory.

Contribution

It presents the first comprehensive introduction of N-algebraic structures and over 200 new definitions, expanding the scope of algebraic research.

Findings

Introduction of N-groups, N-semigroups, N-loops, and N-groupoids

Development of mixed N-algebraic structures

Applications in automata, coloring, and coding theory

Abstract

For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It contains more than 200 new definitions. These concepts find applications in fields like finite automaton, coloring problems and coding theory.