THE LENGTHS OF ARTINIAN MODULES WITH COUNTABLE NOETHERIAN DIMENSIONS

被引：0
|
作者：
Davoudian, M. [1 ]
Ghayour, O. [1 ]
机构：
[1] Shahid Chamran Univ Ahvaz, Dept Math, Ahvaz, Iran
来源：
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2017年 / 43卷 / 06期
关键词：
Artinian module; Noetherian dimension; atomic module; the length of an R-module; DUAL KRULL DIMENSION; DEVIATION; RINGS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that if M is an Artinian module over a ring R, then M has Noetherian dimension alpha, where alpha is a countable ordinal number, if and only if omega(alpha) + 2 <= l(M) <= omega(alpha+1), where l(M) is the length of M, i.e., the least ordinal number such that the interval [0, l(M)) cannot be embedded in the lattice of all submodules of M.
引用
收藏
页码：1621 / 1628
页数：8
相关论文
共 50 条
12345