The main contents of the thesis consist of two independent parts . one is the characterization of weak i sequences in terms of ext functors . we prove that the existence of such sequence and the length of a maximal weak / sequence can be expressed as some vanishing properties of ext functors 本文主要研究工作由两个独立的部分组成，其中一部分是利用ext函子来刻画弱i序列，并且证明了这个序列的存在性，以及极大弱i序列具有同样的长度。
In the third section , using the properties of cocritical modules by the morita context functors , we give the concepts of - prime torsion theories . meanwhile we argue about several properites and the important relationship beetween - prime torsion theories and - prime torsion theories 在第三部分中，我们通过上临界模在moritacontext函子作用下所保持的性质，引入了?素挠理论，再讨论?素挠理论相关性质及与-素挠理论之间的重要关系。
By constructing two functor , we have proved a representation theorem of the category stml that the category stml is equivalent with the category fsts , where fsts is consisted of - fuzzifying scott topological spaces and the mappings which are preserving directed - join and way - below relation and continuous . besides , the category stml ( c ) has been discussed , where c is a subcategory of the category of the completely distributive lattices and gohs , c , morphisms are ( 1 , 2 ) - smooth continuous goh 构造性地给出一对函子，并以此证明了范畴stml ( l )的一个表示定理，即范畴stml ( l )与范畴fsts ( l ) (由l - fuzzifyingscott拓扑空间与保定向并和way - below关系的l - fuzzifying连续映射所构成的范畴)等价。
Hereditary torsion theories have been developed since the 1960 ' s and have been extensively studied by golan , gabriel , dickson , stenstrom , etc . in this thesis , combining hereditary torsion theories with morita contexts , we discuss the changes of some properties about hereditary torsion theories by the morita context functors and the covers and envelopes by a special category 本文主要将遗传挠理论同moritacontexts结合，讨论在moritacontext函子作用下关于遗传挠理论的一些基本性质的转移及变化，并通过一类特殊的模范畴对包与盖进行探讨
An important property of sobrification is given . by discussing the spectra of complete lattices , a theoretical foundation of sobrification of spaces is obtained . thus we know that the category of sober spaces is a reflective subcategory of the category of all the topological spaces with continuous functions 通过对完备格的谱理论的简单讨，为一般的拓扑空间及偏序集的sober匕做了理论上的铺垫z指出了拓扑空间的sober化函子是从sob到top的包含函子的左拌随，理想完备化函子是从alg到pos的遗忘函子的左拌随
In the last section , we discuss the covers and envelopes both of which are of great importance in the field of ring theories . by the morita context functors we can transform from rx - cover ( envelope ) into sx - f - cover ( envelope ) . finally they are further characterized by the particular properties of the direct limit 在第四部分中，我们对环论中十分重要的内容? ?包与盖进行探讨，通过一类特殊的模范畴_ rx ( _ sx ) ，使_ rx -包(盖)在moritacontext函子作用下转化为_ sx -包(盖) ，最后利用正向极限的特性，进一步刻画这类特殊的包与盖。
