Rings with divisibility on chains of ideals

被引：7

作者：

Dastanpour, R. ^{[1
]}

Ghorbani, A. ^{[1
]}

机构：

[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 07期

关键词：

Ascending chain condition; descending chain condition; regular ring; semisimple artinian ring;

D O I：

10.1080/00927872.2016.1233227

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a generalization of the ascending and descending chain condition on one-sided ideals by means of divisibility on chains. We say that a ring R satisfies ACC(d) on right ideals if in every ascending chain of right ideals of R, each right ideal in the chain, except for a finite number of right ideals, is a left multiple of the following one; that is, each right ideal in the chain, except for a finite number, is divisible by the following one. We study these rings and prove some results about them. Dually, we say that a ring R satisfies DCCd on right ideals if in every descending chain of right ideals of R, each right ideal in the chain, except for a finite number of right ideals, is divisible by the previous one. We study these conditions on rings, in general and in special cases.

引用

页码：2889 / 2898

页数：10