分次环的Smash积A # G~*与单位分量A_e理想间的对应

Correspondence between Ideals of A #G~* and Indeals of A_e for Graded Ring A

本文对任意群Ｇ上的任意分次环Ａ，建立了Ｓｍａｓｈ积Ａ＃Ｃ＊和单位分量Ａｅ理想同的对应关系，并运用所建立的对应关系研究分次环的Ｓｍａｓｈ积Ａ＃Ｇ＊和Ａｅ的半素性，素性和单性。

M. Cohen and S. Montgomery built the corresponding relations between ideals of the smash product A # G and ideals of the identity component A_e for a ring A graded by a finite group G. It is goal of this paper to give the corresponding relations for any group-graded ring, and to apply it to investigate the semisimplicity primeness and primitiveness of the smash product A#G and A_e for a graded ring A.