CHAIN CONDITIONS ON NON-PARALLEL SUBMODULES

被引：0
作者：
Shirali, Nasrin [1 ]
Maschizadeh, Mohammad [1 ]
Javdannezhad, Sayed Malek [2 ]
机构：
[1] Shahid Chamran Univ Ahvaz, Dept Math, Ahvaz, Iran
[2] Shahid Rajaee Teacher Training Univ, Dept Math, Fac Sci, Tehran, Iran
来源：
INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA | 2025年 / 37卷
关键词：
Parallel submodule; type dimension; np-Noetherian module; np- Artinian module; iso-Noetherian module; iso-Artinian module; MODULES;
D O I：
10.24330/ieja.1531556
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
. In this paper, we investigate modules with ascending and descending chain conditions on non-parallel submodules. We call these modules npNoetherian and np-Artinian respectively, and give structure theorems for them. It is proved that any np-Artinian module is either atomic or finitely embedded. Also, we give a sufficient condition for np-Noetherian (resp., np-Artinian) modules to be Noetherian (resp., Artinian). We study ascending (resp., descending) chain condition up to isomorphism on non-parallel submodules as npi-Noetherian (resp., npi-Artinian) modules and characterize these modules. It is shown that any npi-Noetherian module has finite type dimension. Next, we investigate some properties of semiprime right np-Artinian (resp., npiArtinian) rings. In particular, it is proved that if R semiprime ring such that J(R) is not atomic, then R is right np-Artinian if and only if it is semisimple. Further, it is shown that if R is a semiprime right npi-Artinian ring, then either Z(R) is atomic or R is right non-singular. Finally, we investigate when nprings coincide.
引用
收藏
页码：249 / 272
页数：24
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