分次环的有限正规扩张

FINITE NORMALIZED EXTENSIONS OF GRADED RINGS

本文研究了群分次环的有限正规分次扩张问题.利用经典环论方法,得到一个群分次环与其有限正规分次扩张环之间关于分次Jacobson根和分次素根的关系,同时,给出了分次情形的Cutting down定理和Lying over定理.

In this Paper we investigate the problems of finite normalized graded extension of group graded rings. Making use of the classical methods in ring theory, we obtain the relations with regard to graded Jacobson radical and graded prime radical between a group graded ring and its finite normalized graded extension ring. Meanwhile, we present the graded versions of Cutting down theorem and Lying over theorem.