JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (4): 24-30.doi: 10.6040/j.issn.1671-9352.0.2017.581

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

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

  1. 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

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

CLC Number: 

  • O154
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