injective resolution meaning in English
单射分析
内射分解, 单射分解
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。