一些中性代数结构和中性N-代数结构
Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures
摘要：
在这本书中，我们第一次介绍的概念，代数结构的群体，循环，半群和群胚;也是他们的代数N-代数结构。人们充分意识到这样一个事实，即许多经典定理，如拉格朗日，西洛和柯西已研究的背景下，有限群。在这里，我们试图通过研究和引入这些定理的代数半群，代数广群胚，代数环转移的范式。本书共有七章。第一章提供了几个基本概念，使本书自成一体。第二章介绍了代数群和代数N-群，并给出了几个例子。第三章研究了代数半群和代数N-半群，给出了几个有趣的结果。第四章介绍了代数环和代数N-环。我们引入了几个新的、相关的定义。实际上，我们利用模整数Z_n，n > 3（n为奇数）构造了一类新的代数环。这些结构的几个性质证明使用数论技术。第五章介绍了代数群胚和代数N-群胚的概念。第六章创新性地给出了混合式隐喻结构及其语义特征。最后一章提出了问题供感兴趣的读者解决。
英文摘要：
In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids; and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many classical theorems like Lagrange, Sylow and Cauchy have been studied only in the context of finite groups. Here we try to shift the paradigm by studying and introducing these theorems to neutrosophic semigroups, neutrosophic groupoids, and neutrosophic loops. This book has seven chapters. Chapter one provides several basic notions to make this book self-contained. Chapter two introduces neutrosophic groups and neutrosophic N-groups and gives several examples. The third chapter deals with neutrosophic semigroups and neutrosophic N-semigroups, giving several interesting results. Chapter four introduces neutrosophic loops and neutrosophic N-loops. We introduce several new, related definitions. In fact we construct a new class of neutrosophic loops using modulo integer Z_n, n > 3, where n is odd. Several properties of these structures are proved using number theoretic techniques. Chapter five just introduces the concept of neutrosophic groupoids and neutrosophic N-groupoids. Sixth chapter innovatively gives mixed neutrosophic structures and their duals. The final chapter gives problems for the interested reader to solve.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
