单位理想稳定秩(英文)

On Unit Ideal-Stable Ranges

设I是环R的理想.证明R满足单位〈I〉-稳定秩当且仅当R满足单位[I]-稳定秩,当且仅当R满足单位(I)-稳定秩且I有稳定秩1,并将结论应用到正则理想以及矩阵环等相关情形,获得R满足单位〈I〉-稳定秩的一系列等价条件.

Let I be an ideal of a ring R. It＇s proved that R satisfies unit （1）-stable range if and only if R satisfies unit [I] -stable range, if and only if R satisfies unit （I） -stable range and I has stable range one. Some applications are also obtained.