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

作　　者：陈东 王芳贵[2] 蹇红[2] 陈明钊 CHEN Dong;WANG Fang-gui;JIAN Hong;CHEN Ming-zhao(College of Information Science and Engineering, Chengdu University, Chengdu 610106, Sichuan, China;College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Siehuan, China)

机构地区：[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

出　　处：《山东大学学报（理学版）》2018年第4期24-30,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11671283)

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

关 键 词：2-强Gorenstein半单环 模的直和分解 秩 信息位数 

分 类 号：O154[理学—数学]