分次环，A，A_e和Smash积A＃G是亚直既约环的条件

Conditions for a Graded Ring A、A e and Smash Product A#G * to be Subdirectly Irreducible Rings

讨论了分次环Ａ，Ａｅ和Ａ＃Ｇ＊的相关性质，在Ａ是分次忠实时，Ａ＃Ｇ＊是亚直既约环当且仅当Ａｅ是亚直既约环；在Ａ是分次非退化时，Ａ＃Ｇ＊是Ｇ亚直既约环当且仅当Ａ是分次亚直既约环．

This paper deals with some retative properties of A and smash product A#G * ; when A is graded faithful, A#G * is subdirectly irreducible ring if and only if A e is also. When A is Graded nondegenerate, A#G * is G subdirectly irreducible ring if and only if A is Graded subdirectly irreducible ring.