最小理想與最小左理想的概念在環論與近環裡扮演著重要的角色，為了研究更深層的結果，會需要使用雅各布森根基的概念。在這篇文章裡，我們會探討近環的根基與其衍伸出來好的結果，我們還會給出非交換環論裡的一些結果與證明。

The concept of minimal ideals and minimal left ideals plays a dominant
role in ring and nearring theory. To study deeper results on this
concept demands some powerful tools. Therefore, the idea of the radical
in ring and nearring theory is essential. In ring theory, one of the
importance of the Jacobson radical J(R) lies in the fact that every
nil left ideal and every nil right ideal in R is contained in J(R).

Nearrings is a generalization of rings which arise naturally from
mappings on groups. Since every ring is a nearring, the true statements
in nearrings are useful in ring theory. In this article, the radicals
for nearrings and their good properties will be discussed. Moreover,
some results in noncommutative ring theory will be proved in this
article.

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