2-强Gorenstein半单环上模的结构及其应用

doi:10.6040/j.issn.1671-9352.0.2017.581

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (4): 24-30.doi: 10.6040/j.issn.1671-9352.0.2017.581

2-强Gorenstein半单环上模的结构及其应用

陈东¹,王芳贵²,蹇红²,陈明钊²

1.成都大学信息科学与工程学院, 四川成都 610106;2.四川师范大学数学与软件科学学院, 四川成都 610066

收稿日期:2017-11-14 出版日期:2018-04-20 发布日期:2018-04-13
作者简介:陈东(1983— ),男,硕士,讲师,研究方向为交换代数与同调代数. E-mail:chendong@cdu.edu.cn
基金资助:
国家自然科学基金资助项目(11671283)

Structure of modules over 2-strongly Gorenstein semisimple ring with its application

CHEN Dong¹, WANG Fang-gui², JIAN Hong², CHEN Ming-zhao²

1. College of Information Science and Engineering, Chengdu University, Chengdu 610106, Sichuan, China;
2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan, China

Received:2017-11-14 Online:2018-04-20 Published:2018-04-13

摘要/Abstract

摘要： 研究了局部2-强Gorenstein半单环上任一模M的结构,证明了M可以唯一分解为不可分解模的直和。利用模M的直和分解,引入了有限生成模M的秩rank(M)的概念,证明了在有限局部2-强Gorenstein半单环上这样定义的秩就是线性码的信息位数。

关键词: 模的直和分解, 秩, 2-强Gorenstein半单环, 信息位数

Abstract: The structure of the module M over the local 2-strongly Gorenstein semisimple ring is investigated. Namely, M is uniquely decomposed into a direct sum of indecomposable modules. By the decomposition of M into direct sum, the definition of the rank of finitely generated module M is introduced. It is proved that, the rank defined over the local 2-strongly Gorenstein semisimple ring is the information bit of the linear codes.

Key words: 2-strongly Gorenstein semisimple ring, information bit, direct sum decomposition of modules, rank

中图分类号:

O154

陈东,王芳贵,蹇红,陈明钊. 2-强Gorenstein半单环上模的结构及其应用[J]. 山东大学学报（理学版）, 2018, 53(4): 24-30.

CHEN Dong, WANG Fang-gui, JIAN Hong, CHEN Ming-zhao. Structure of modules over 2-strongly Gorenstein semisimple ring with its application[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 24-30.

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2-强Gorenstein半单环上模的结构及其应用

Structure of modules over 2-strongly Gorenstein semisimple ring with its application

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