Commutative Coherent Rings
Commutative Coherent Rings
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DOI：
10.1007/bfb0084570
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发表时间：
1989-08
影响因子：
7.6
通讯作者：
Sarah Glaz
中科院分区：
文献类型：
--
作者：
Sarah Glaz
这本书提供了第一次广泛和系统的治疗理论的交换连贯环。它融合，并提供了一个链接，在两个有时不相交的方法，在文献中，环理论的方法，和同调代数的方法。这本书涵盖了大多数结果交换连贯环理论已知的日期，以及一些结果从未发表过。从基本结果开始，这本书的主题，如：一致的连贯性，经常环，环的小同调维数，多项式和幂级数环，群环和对称代数的连贯环。连贯性的主题被带到了研究的前沿，暴露了该领域的开放性问题。大多数主题都是在其充分的一般性，得出的结果一致环的结论一般理论。因此，这本书开发了许多工具的现代研究交换代数与各种例子和反例。虽然这本书基本上是独立的，交换和同调代数的基本知识是推荐的。它面向研究生和研究人员。
This book provides the first extensive and systematic treatment of the theory of commutative coherent rings. It blends, and provides a link, between the two sometimes disjoint approaches available in the literature, the ring theoretic approach, and the homological algebra approach. The book covers most results in commutative coherent ring theory known to date, as well as a number of results never published before. Starting with elementary results, the book advances to topics such as: uniform coherence, regular rings, rings of small homological dimensions, polynomial and power series rings, group rings and symmetric algebra over coherent rings. The subject of coherence is brought to the frontiers of research, exposing the open problems in the field. Most topics are treated in their fully generality, deriving the results on coherent rings as conclusions of the general theory. Thus, the book develops many of the tools of modern research in commutative algebra with a variety of examples and counterexamples. Although the book is essentially self-contained, basic knowledge of commutative and homological algebra is recommended. It addresses graduate students and researchers.