具有Krull维数的半素环

A Semiprime Ring with Krull Dimension

本文讨论了半素环的闭理想性质,引进了强Kasch环的概念并给出半素环是强Kasch环的充分必要条件,最后讨论了强Kasch半素环上具有Krull维数的模的内射包络的自同态环。

This paper is divided into three sections. The first section investigates the properties of closed ideals of a semiprime ring. The second section introduces the concept of strongly Kaseh ring and obtains the necessary and sufficient conditions that a semiprime ring is strongly Kasch. The final section investigates the endomorphism ring of injective hull of a module with Krull dimension over the strongly Kasch semiprime ring.