分次zip环与SPlit-null扩张(英文)

Graded Zip Rings and Split-null Extensions

本文定义并讨论了分次zip环,讨论了交换环的Split—null扩张的zip性,推广了C.Faith的部分结果。

A ring R is Called to be zip ring if for any subset S R, rR(S) = {r ∈ R|Sr = 0} = 0=> rR(S1) = 0 for some finite subset S1 of S.In our paper, graded zip ring is defined and discussed, the following results are proved: for a graded ring R with nondegonerate gvading, R is graded zip ring iff Re is a zip ring; for a commutative ring R, and a finite abel group G, R is a zip ring iff the smash product R#G is a zip ring. Using those results we discuss the split-null extension R = B × E of B. Some results in [2] are extended.