由于概念和技术上的困难，热带（Tropical）代数理论的研究仍处于初级阶段。前人已获得的有关研究成果，展示了该领域内许多有趣的现象和研究的魅力与艰辛。正如曼切斯特大学Johnson和莫斯科国立大学Shitov等教授指出的：创立整体上相对成熟的热带代数的半群理论是一项具有重大挑战的工作。基于前期工作，结合国际研究趋势，本项目将面对挑战，继续研究热带代数理论，具体研究内容为：将现代半群代数理论中的结果与方法引入到这一理论研究之中，研究热带矩阵半群和半环的性质、特征和结构；把2-闭置换群看做热带矩阵半群的子群展开深入的研究；力图通过热带代数的方法路径，解答有关2-闭置换群的几个公开问题与猜想；研究正规热带矩阵半环的结构；探索它们的代数性质与几何性质。本项目的实施将会进一步丰富和完善热带代数理论，也将会在热带几何和理论计算机科学等相关学科中找到好的应用，开创我国在该研究领域的新局面。

Due largely to the difficulties, both conceptual and technical, of the subject, the study of Tropical algebraic theory is still in its infancy. The relevant research results in the literature have demonstrated a number of interesting phenomena, the charm and hardship of the research in this field. As Professors Johnson and Kambites in Manchester of University and Professor Shitov in Moscow State University have pointed out, the development of a coherent and comprehensive theory of tropical matrix semigroups of arbitrary finite dimension is a major challenge. Based on our previous work and the current international research trends, this project will face challenges and continue to study Tropical algebra theory. The specific research contents are as follows: introduce the results and methods of modern semigroup algebra theory into the study of Tropical algebra theory, study the properties, characteristics and structures of semigroups and semirings of Tropical matrices; regarded 2-closed permutation groups as subgroups of Tropical matrix semigroups, study in depth them; by Tropical algebraic method, solve several open questions and conjectures about 2-closed permutation groups; study the structure of normal Tropical matrix semirings, explore their algebraic and geometric properties. The implementation of this project will further enrich and improve Tropical algebra theory, find good applications in Tropical geometry and theoretical computer science and other disciplines, and open up a new situation in this field in China.