主理想整环上有限生成模之子模与商模之结构

主理想整环上有限生成模之子模与商模之结构 Structure of Submodules and Factors Modules of a Finitely Generated Module over a Principal Ideal Domain 李卫峰 LI Weifeng 1 first-author 中国地质大学(武汉)数学与物理学院 中国地质大学(武汉)数学与物理学院 School of Mathematics and Physics,China University of Geosciences School of Mathematics and Physics,China University of Geosciences 考虑了主理想整环上有限生成模之子模与商模之结构,详细讨论了将模分解成循环子模的直和且循环子模的阶理想满足包含关系时,相应的阶理想与子模或商模相应分解对应的阶理想之间的关系——即前者能控制后者. In this paper,we discuss the structures of the submodules and factor modules of a finitely generated module over a p.i.d（principal ideal domain）,and we discuss in detail the relations between the order ideals of the module which factoring as cyclic submodule whose order ideals satisfies the inclusion relations and the order ideals of the sbmodules and factor modules which factoring as cyclic submodule whose order ideals satisfies the inclusion relations,i.e.,the former can control the latter.The method used here is different from that of the classic of N Jacobson. 主理想整环 有限生成模 阶理想 p.i.d（principal ideal domain） finitely generated module order ideal 10.14188/j.1671-8836.2015.04.005 O153.3 中央高校基本科研业务费专项资金资助（CUGL110234） 2015-04-01 2021-03-31 4 61