内射分解 meaning in English
injective resolution
Examples
- 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 。 - Since the k - gorenstein property of ring r x m is an important aspect in the research field , in the first chapter , we have got an equivalent condition for r m as a k - gorenstein ring by study the injective resolution of ring r m . the dimensions of rings is one of the most important parts in homological theory
在第一章，我们通过对r ( ? ) m内射分解的考察得到了r ( ? ) m成为k - gorenstein环的一个充分必要条件：维数的研究是同调理论中的核心部分，伴随同调理论的形成，它便一直成为同调代数中研究的焦点。 - 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。