主理想整环上有限生成模结构定理的新证明  

A New Approaches to the Structure of a Finitely Generated Module on a Principal Ideal Domain

作　　者：石生明 朱一心[1] SHI Sheng-ming;ZHU Yi-xin(School of Mathematical Sciences,Capital Normal University,Beijing 100048,China)

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《数学的实践与认识》2022年第5期230-245,共16页Mathematics in Practice and Theory

摘　　要：通常研究主理想整环上有限生成模的途径是把它看成自由模的商模.由它的生成元的定义关系出发,引入完备关系组和定义关系矩阵,直接证明了主理想整环上有限生成模的两个结构定理,还得到了与定义关系矩阵有关的其它新结论.This paper gives a new way to find out the structure of a finitely generated module on a principal ideal domain,using definition relations of its generators and matrix of definition relations,while the known proofs of the results have to depend on the quotient module of a free module.For torsion module,some properties of matrix of definition relations are given.

关 键 词：主理想整环上有限生成模 直和分解 零化理想 循环子模 

分 类 号：O153.3[理学—数学]