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A Singular Introduction to Commutative Algebra / by Gert-Martin Greuel, Gerhard Pfister
版 | 2nd ed. 2008. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2008 |
本文言語 | 英語 |
大きさ | XX, 689 p : online resource |
著者標目 | *Greuel, Gert-Martin author Pfister, Gerhard author SpringerLink (Online service) |
件 名 | LCSH:Algebra LCSH:Algebraic geometry LCSH:Algorithms LCSH:Mathematics -- Data processing 全ての件名で検索 LCSH:Computer science -- Mathematics 全ての件名で検索 FREE:Algebra FREE:Algebraic Geometry FREE:Algorithms FREE:Computational Mathematics and Numerical Analysis FREE:Symbolic and Algebraic Manipulation |
一般注記 | Rings, Ideals and Standard Bases -- Modules -- Noether Normalization and Applications -- Primary Decomposition and Related Topics -- Hilbert Function and Dimension -- Complete Local Rings -- Homological Algebra From the reviews: "…It is certainly no exaggeration to say that Greuel and Pfister's A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra, in which computational methods and results become central to how the subject is taught and learned. […] Among the great strengths and most distinctive features of Greuel and Pfister's book is a new, completely unified treatment of the global and local theories. The realization that the two cases could be combined to this extent was decisive in the design of the Singular system, making it one of the most flexible and most efficient systems of its type. The authors present the first systematic development of this unified approach in a textbook here, and this aspect alone is almost worth the price of admission. Another distinctive feature of this book is the degree of integration of explicit computational examples into the flow of the text. Strictly mathematical components of the development (often quite terse and written in a formal "theorem-proof" style) are interspersed with parallel discussions of features of Singular and numerous Singular examples giving input commands, some extended programs in the Singular language, and output. […] Yet another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic. A synopsis of the table of contents will make this clear. […] Greuel and Pfister have written a distinctive an highly useful book that should be in the library of every commutative algebrais and algebraic geometer, expert and novice alike. I hope that it achieves the educational impact it deserves." John B. Little, Monthly of The Mathematical Association of America, March 2004 "... The authors' most important new focus is the presentation of non-well orderings that allow them the computational approach for local commutative algebra. In fact the book provides an introduction to commutative algebra from a computational point of view. So it might be helpful for students and other interested readers (familiar with computers) to explore the beauties and difficulties of commutative algebra by computational experiences. In this respect the book is the one of the first samples of a new kind of textbooks in algebra." P.Schenzel, Zentralblatt für Mathematik 1023.13001, 2003 HTTP:URL=https://doi.org/10.1007/978-3-540-73542-7 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783540735427 |
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EB00232058 |
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