Methods of Algebraic Geometry
Methods of Algebraic Geometry
复制标题
作者：
J. Todd
“这本书是本书的第一部分，旨在为现代代数几何的基础和方法提供方便的说明。”作者序言中的这些文字解释了本书的范围并解释了所讨论主题的选择。近年来，越来越明显的是，代数几何的严格处理必须在比该学科的经典描述更大的程度上建立在代数原理的基础上。因此，所讨论的书中超过三分之一的内容都是纯代数的，这一点不足为奇。事实上，前四章对代数域、多项式和矩阵（在不一定可交换的基本域上）理论进行了清晰而简洁的介绍。这个叙述本身是最有价值的，因为现代代数观点在许多英语著作中找不到，尽管有一些叙述已经在美国出版。
“THIS volume is the first part of a work designed it provide a convenient account of the foundations and methods of modem algebraic geometry.” These words from the authors' preface explain the scope of the present volume and account for the selection of topics treated. It has become increasingly clear in recent years that a rigorous treatment of algebraic geometry must be based, to a much greater extent than the classical accounts of the subject, on algebraic principles. It is therefore no occasion for surprise that more than a third of the volume under discussion is purely algebraic. The first four chapters constitute, in fact, a clear and concise introduction to the theory of algebraic fields, polynomials and matrices (over a ground field which is not necessarily commutative). This account is in itself most valuable, since the modem point of view in algebra is not to be found in many English works, though several accounts have been published in the United States.