Serial Right Noetherian Rings
Serial Right Noetherian Rings
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系列右诺特环
DOI：
10.4153/cjm-1984-003-5
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
Surjeet Singh
中科院分区：
文献类型：
--
作者：
Surjeet Singh
一个模M称为序列模，如果它的子模族在包含下是线性序的。一个环R称为串行的，如果RR以及RR是串行模的有限直和。Nakayama [8]开始了对Artin序列环的研究，他称之为广义unisbranding环。Murase [5，6，7]证明了关于广义unisbringing的若干结构定理，并且他用除环上的拟矩阵环描述了其中的大部分。沃菲尔德[12]研究了序列双侧Noether环，并证明了任何这样的不可分解环要么是Artin环，要么是素环。他进一步证明了双侧Noether素序列环是（R：J）-块上三角矩阵环，其中R是具有Jacobson根J的离散赋值环.本文确定了序列右Noether环的结构（定理2.11）.
A module M is called a serial module if the family of its submodules is linearly ordered under inclusion. A ring R is said to be serial if RR as well as RR are finite direct sums of serial modules. Nakayama [8] started the study of artinian serial rings, and he called them generalized uniserial rings. Murase [5, 6, 7] proved a number of structure theorems on generalized uniserial rings, and he described most of them in terms of quasi-matrix rings over division rings. Warfield [12] studied serial both sided noetherian rings, and showed that any such indecomposable ring is either artinian or prime. He further showed that a both sided noetherian prime serial ring is an (R:J)-block upper triangular matrix ring, where R is a discrete valuation ring with Jacobson radical J. In this paper we determine the structure of serial right noetherian rings (Theorem 2.11).