【摘要】 提出半环、半模、余关系等概念,给出了半模的子半模关系之间的对应关系,并由余关系导出强半模和单半模的概念,得到半环和.研究半模的同构及余关系对应定理、Schur引理以及半模是单半模和半模的子半模是单半模的充分必要条件.更多还原

【Abstract】 In this paper,semirings,semimodules and congruence relations are defined,and following the correspondence between subsemimodules of semimodules and their congruence relations,strong semimodules and simple semimodules are induced.We get the isomorphisms of semirings(semimodules) and their congruence relations′ correspondence theorem,Schur′s Lemma, and necessary and sufficient conditions of semimodules to be simple and subsemimodules of semimodules to be simple.更多还原