Serial Right Noetherian Rings

Author:

Singh Surjeet

Abstract

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).

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 25 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the Restricted Minimum Condition for Rings;Mediterranean Journal of Mathematics;2020-11-21

2. Serial Nonsingular Rings. Jacobsons’s Conjecture;Algebras, Rings and Modules;2016-04-05

3. On Serial Noetherian Rings;Communications in Algebra;2006-10

4. Serial Rings with T-Nilpotent Prime Radical;Algebras and Representation Theory;2006-04

5. Serial and semidistributive modules and rings;Handbook of Algebra;2000

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