ON PRIME ONE-SIDED IDEALS, BI-IDEALS AND QUASI-IDEALS OF A GAMMA RING

被引：2

作者：

BOOTH, GL ^{[1
]}

GROENEWALD, NJ ^{[1
]}

机构：

[1] UNIV PORT ELIZABETH,PORT ELIZABETH 6000,SOUTH AFRICA

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS | 1992年 / 53卷

关键词：

D O I：

10.1017/S1446788700035394

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a GAMMA-ring with right operator ring R. We define one-sided ideals of M and show that there is a one-to-one correspondence between the prime left ideals of M and R and hence that the prime radical of M is the intersection of its prime left ideals. It is shown that if M has left and right unities, then M is left Noetherian if and only if every prime left ideal of M is finitely generated, thus extending a result of Michler for rings to GAMMA-rings. Bi-ideals and quasi-ideals of M are defined, and their relationships with corresponding structures in R are established. Analogies of various results for rings are obtained for GAMMA-rings. In particular we show that M is regular if and only if every bi-ideal of M is semi-prime.

引用

页码：55 / 63

页数：9