HX环与幂环

HX ring and power ring

群的代数结构的提升,为一般代数系统的代数结构的提升提供了一种研究方法,于是人们自然会想到环的代数结构的提升问题.1988年,李洪兴教授首次提出了HX环[1]的概念,开始了环代数结构的提升.2000年,钟育彬[2]给出了非平凡HX环的例子,说明了非平凡HX环的存在性.本文建立了一般的HX环与幂环的构造理论,同时还给出一些非平凡HX环与非平凡幂环的例子.

With the upgrade of algebraic structures of groups, people think of the upgrade of algebraic structures of other algebraic systems, such as rings, modules, lattices, and so on, Li Hongxing first considered the upgrade of algebraic structures of rings in 1988, and raised the concept of HX rings, and then some scholars have obtained a lot of significant results about HX rings. Zhong Yubin has proved the existence of non-trivial HX rings . In this paper, we put forward the constructic theories of generalized HX ring and power ring, and gave some examples of non-trivial HX rings and power rings,