强分次环上全矩阵环的一类子环的理想格

Ideal Lattices of Subring of Complete Matrix Ring over Strongly Group Graded Ring

设为强G-分次环,表示G上n阶方阵所成的集合,我们证明了M_G(R)的子环的理想格与R的子环R(H)的理想格之间存在1-1对应关系.给出了smash积R#G成为Artin单环的一个充分必要条件,最后我们讨论了R{H}的分次结构,证明了上面的对应关系亦是R{H}的分次理想集与R{H}的分次理想集之间的1-1对应。

We give a faithful function between ideal lattices of subring of complete matrix ring and subring of fimite group graded ring as strongly grading Finally,we study their graded comstructions,show the preceding function is also one-to-one between the sets of graded ideal of subring.