AI 中文总结
本文提出近环的一种扩张理论,其半直和为特例,近环理论中已有不少相关构造实例,丰富了近环的研究方法。
AI 中文摘要
本文给出了近环的一种扩张理论,其思路源于群的Schreier扩张与环的Everett扩张。两个近环的半直和是该理论的一个特例,近环理论中已有许多专为构造近环设计的实例属于该半直和构造。
英文摘要
An extension theory for nearrings along the lines of the Schreier extension for groups and the Everett extension for rings is given. The semidirect sum of two nearrings is a special case of this theory. Already there are many examples of purpose built nearring constructions in the theory of nearrings which fall under this semidirect sum construction.