单投射半模和拟单内射半模的若干研究

发布时间：2018-11-08 15:39

【摘要】：本文主要研究单投射半模、单内射半模和拟单内射半模.全文由四个部分构成:第一部分是预备知识,列出了本文涉及的相关定义及命题.第二部分在投射半模的基础知识上引进了单投射半模的概念,主要探究了单投射半模的性质,如单投射半模P与HomR(P,-)函子的关系,单投射半模(?)APi与直和项Pi的关系;然后证明了若投射半模M的商半模是内射半模,则M的任意单子半模必为M-单投射半模;接着给出了M-单投射半模与k M--投射半模的等价条件;最后证明了相对于单投射半模的Schanuel引理.第三部分在内射半模上引入了单内射半模的概念,探究单内射半模的性质,最后也证明了相对于单内射半模的Schanuel引理.第四部分,探究一类特殊的单内射半模即拟单内射半模,主要给出了拟单内射半模的等价判定.
[Abstract]:In this paper, we study single projective semimodules, simple injective semimodules and quasi simple injective semimodules. This paper is composed of four parts: the first part is the preparatory knowledge, which lists the relevant definitions and propositions involved in this paper. In the second part, the concept of single projective semimodule is introduced into the basic knowledge of projective semimodule. The properties of single projective semimodule, such as the relation between single projective semimodule P and HomR (Pn-) functor, are studied. The relationship between single projective semimodule (?) APi and direct sum term Pi; Then it is proved that if the quotient semimodule of a projective semimodule M is an injective semimodule, then any single submodule of M must be a M-simple projective semimodule, and then the equivalent conditions of M-simple projective semimodule and k M-projective semimodule are given. Finally, we prove the Schanuel Lemma relative to a simple projective semimodule. In the third part, we introduce the concept of simple injective semimodules on injective semimodules, investigate the properties of simple injective semimodules, and finally prove the Schanuel Lemma relative to simple injective semimodules. In the fourth part, we discuss a special kind of simple injective semimodules, that is, quasi-simple injective semimodules, and mainly give the equivalent judgment of quasi-simple injective semimodules.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.3

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