LDR 02882nac  22003371u 4500
010    _a9780821838044
090    _a8687
101    _aeng
102    _aUS
100    _a20091130              frey50       
200    _aAn introduction to Grobner bases
       _fWilliam W. Adams, Philippe Loustaunau
210    _aProvidence
       _cAmerican Mathematical Society
215    _a1 vol. (XIII-289 p.)
225    _aGraduate studies in mathematics
320    _aBibliogr. p. 279-281. Index
330    _aChapters: 1. Basic theory of Gröbner bases, 2. Applications of Gröbner bases, 3. Modules and Gröbner bases, 4. Gröbner bases over rings.

The books begins on a very elementary level and introduces the polynomial arithmetic, the properties of Gröbner bases and Buchberger’s algorithm very carefully. The introduction is accompanied by several complete examples for the application of the algorithms. A significant part of the book is devoted to applications of the Gröbner bases. The book does not try to cover the complete field of computational ideal theory. Aspects like dimension theory, related algorithm methods, complexity, technology are redirected to different sources.

The rich set of applications and exercises concentrates on pure higher algebra. Especially the chapters on modules and bases over rings present material which is usually not available in that compact form. – The book is intended as a textbook for advanced undergraduates. It could have served also as a handbook for problems related to polynomial ideal algebra; however, the solutions of the numerous non-trivial problems are not included. The Gröbner base technique is handled on a pure theoretical level. Its limitations, especially the expression swell and the maximal sizes of practically computable problems are not mentioned. (Zentralblatt)
410    _9172714
       _tGraduate studies in mathematics
676    _a2010
686    _a13P10
       _bCommutative algebra -- Computational aspects and applications
       _xGröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
686    _a13-02
       _bCommutative algebra
       _xResearch exposition (monographs, survey articles)
686    _a13F20
       _bCommutative algebra -- Arithmetic rings and other special rings
       _xPolynomial rings and ideals; rings of integer-valued polynomials
700    _4070
       _bWilliam W.
701    _4070
856    _uhttp://zbmath.org/?q=an:0803.13015
856    _uhttp://www.ams.org/mathscinet-getitem?mr=1287608
856    _uhttp://www.ams.org/bookstore-getitem/item=GSM-3
905    _agf
906    _aaw
906    _aaw
995    _f11490-01
       _k13 ADA
       _eSalle R
001     8687
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