A Singular Introduction to Commutative Algebra
Autor Gert-Martin Greuel, Gerhard Pfisteren Limba Engleză Hardback – 5 noi 2007
"It is certainly no exaggeration to say that … A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra … . Among the great strengths and most distinctive features … is a new, completely unified treatment of the global and local theories. … making it one of the most flexible and most efficient systems of its type....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....Greuel and Pfister have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike."
J.B. Little, MAA, March 2004
The second edition is substantially enlarged by a chapter on Groebner bases in non-commtative rings, a chapter on characteristic and triangular sets with applications to primary decomposition and polynomial solving and an appendix on polynomial factorization including factorization over algebraic field extensions and absolute factorization, in the uni- and multivariate case.
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Specificații
ISBN-10: 3540735410
Pagini: 712
Ilustrații: XX, 689 p.
Dimensiuni: 160 x 241 x 43 mm
Greutate: 1.17 kg
Ediția:Second Edition 2008
Editura: Springer
Locul publicării:Berlin, Heidelberg, Germany
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Notă biografică
Gert-Martin Greuel: Born 1944, Studies of Mathematics and Physics at Univ. Göttingen and ETH Zürich, Diploma 1971, PhD 1973 (Göttingen) and Habilitation 1980 in Mathematics (Bonn), 1980–1981 Professor at Univ. Osnabrück (C3), 1981–2010 Professor Univ. Kaiserslautern (C4), 2010 – 2015 Distinguished Senior Professor at Univ. Kaiserslautern, 2015 Emeritus. 2002 – 2013 Director of Mathematisches Forschungsinstitut Oberwolfach, 2009 Dr.h.c. from Leibniz Univ. Hannover, 2011 Honorary Member of Real Sociedad Matemática Española, 2012 – 2015 Editor-in-Chief of Zentralblatt MATH (zbMATH), 2004 First Richard D. Jenks Prize for Excellence in Software Engineering to the Singular team, 2013 Media Prize Mathematik by Deutsche Mathematiker Vereinigung.
Christoph Lossen: Born in 1967, Study of mathematics and economical sciences at the University of Kaiserslautern, 1994 Diploma in Mathematics, 1998 PhD at the University of Kaiserslautern, 2002 State doctorate (Habilitation), 2002-2006 Assistant Professor (Hochschuldozent) at TU Kaiserslautern, since 2006 Administrative Director of the Department of Mathematics at TU Kaiserslautern (since 2023 University of Kaiserslautern-Landau (RPTU)).
Eugenii I. Shustin: Born 1957, Studies of Mathematics at Leningrad State Univ. and Gorky State Univ., Ms. 1979, PhD 1984 (Leningrad). 1984-87 Assistant Prof. at Gorky Civil Eng. Inst., 1987-92 Associate Prof. Kuibyshev State Univ., 1992-96 Associate Prof. Tel Aviv Univ., 1996-now Full Prof. Tel Aviv University. 1990 Invited lecturer at ICM[1]90, Kyoto, 2002 Bessel Research Award from Alexander von Humboldt Foundation, 2018-now The Bauer-Neuman Chair in Real and Complex Geometry.
Textul de pe ultima copertă
"…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