半模的根与基座的作用
The Function of Radical and Socle of Semimodule

利用半模根和弱基座的理论,对有限生成半模和有限上生成半模进行了讨论,给出了半模M是有限生成的必要条件和半模M是有限上生成的充要条件.
By the theory of semimodular root and weak-socle,the function of weak-socle and radical over finitely generate(cogenerated)semimodule are studied.The necessary condition of semimodule M being finitely generated is obtained,the sufficient and necessary condition of semimodule M being finitely cogenerated is given