E . e . enochs put forword the concepts of injective ( projective or flat ) ( pre ) cover and ( pre ) envelope in the early 1980s " , a lot of articles have studied existence and uniqueness of such ( pre ) covers and ( pre ) envelopes , the property of their kernels or cokernels , and character many special rings . moreover , if such kind of ( pre ) covers or ( pre ) envelopes exist , we can construct a complete injective ( projective or flat ) resolvent ( called resolution when exact ) and a partial injective ( projective or flat ) resolvent , and if r is a ring , we can study the relationship of its left global dimension l . d ( r ) ( or its weak dimension w ( r ) ) and the properties of syzygies ( or cosyzygies ) of a resolvent ( or resolution ) , and the relationship of its left global dimension l . d ( r ) ( or its weak dimension ) and the exactness of a resolvent ( or resolution ) 自八十年代初e . e . enochs首次提出并研究内射(投射、平坦) (预)盖及内射(投射、平坦) (预)包这些概念以来，大批论文研究此类包、盖的存在性、唯一性问题以及它们的核、上核的性质，并据此刻画了一些常见的特殊环；更进一步地，当此类包、盖存在时，我们可构造相应的完全投射(平坦、内射)预解式(当正合时称为完全分解式)以及单边投射(平坦、内射)预解式，研究了环的左(右)总体维数、弱维数与此类分解式的合冲模(或上合冲模)的性质、复形正合性之间的关系。
2.
At first a lot of new characterizations of gorenstein injective modules are given , then the author claim that a ring r is qf if and only if every left ( or right ) r - modules are gorenstein injective , and then show that if r is two - side noetherian , r is n - gorenstein if and only if every n - th cosyzygy of an injective resolution of a left ( and right ) r - module is gorenstein injective if and only if every n - th syzygy of an injective resolvent of a left ( and right ) right module is gorenstein injective . finally , we prove that for an n - gorenstein ring r with n > 0 , every module can be embedded in a gorenstein injective module and the injective dimension of its cokernel is at most n - 1 首先给出了gorenstein内射模的许多新的刻画，推出了环r是qf环当且仅当每个左(右)的r -模的单边内射分解式的第n个上合冲是gorenstein内射模，接着推出了左、右noether环只是n - gorenstein环当且仅当每个左(右)模的单边内射分解式的第n个上合冲是gorenstein内射模当且仅当每个左(右)模的单边内射预解式的第n合冲是gorenstein内射模，最后推出了n - gorenstein环中每个模都可嵌入到一个gorenstein内射模之中，且其上核的内射维数不大于n - 1 。
3.
In the second section , the author studies copure injective modules , which are the kernels of injective precovers . at first the author gives some characterizations of copure injective modules , show many characterizations of reduced copure injective modules , and then study when injective precover is exact . moreover , the author claims that if l . pid ( r ) of a ring is finite , some copure injective modules can be obtained by a resolvent , finally analyze the relationship between syzygies of a resolvent and cosyzygies of a resolution on n - gorenstein rings 第二部分着重研究了上纯内射模，即内射预盖的核，首先给出了上纯内射模的一些等价刻画，然后给出了约化的上纯内射模的等价刻画，接着研究了内射预盖在什么条件下正合，再接着研究了当环的l . pid ( r )有限时由模的内射预(分)解式可得到一些上纯内射模，最后讨论了n - gorenstein环中单边内射预解式的合冲模与单边内射分解式的上合冲模之间的联系。
