LDR 02882nac  22003371u 4500
010    _a9780821838044
       _brel.
090    _a8687
101    _aeng
102    _aUS
100    _a20091130              frey50       
200    _aAn introduction to Grobner bases
       _bM
       _fWilliam W. Adams, Philippe Loustaunau
210    _aProvidence
       _cAmerican Mathematical Society
       _d1994
215    _a1 vol. (XIII-289 p.)
       _d26
225    _aGraduate studies in mathematics
       _v3
       _9172716
       _x1065-7339
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
       _aAMS
       _tGraduate studies in mathematics
       _v0003
       _x1065-7339
676    _a2010
686    _a13P10
       _9161928
       _bCommutative algebra -- Computational aspects and applications
       _xGröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
       _20
686    _a13-02
       _9161828
       _bCommutative algebra
       _xResearch exposition (monographs, survey articles)
       _20
686    _a13F20
       _9161887
       _bCommutative algebra -- Arithmetic rings and other special rings
       _xPolynomial rings and ideals; rings of integer-valued polynomials
       _20
700    _4070
       _aAdams
       _bWilliam W.
       _f1937-
       _9175273
701    _4070
       _aLoustaunau
       _bPhilippe
       _f1958-
       _9175274
856    _uhttp://zbmath.org/?q=an:0803.13015
       _zZentralblatt
856    _uhttp://www.ams.org/mathscinet-getitem?mr=1287608
       _zMathScinet
856    _uhttp://www.ams.org/bookstore-getitem/item=GSM-3
       _zAMS
905    _agf
       _b1997
906    _aaw
       _b2011-03-15
906    _aaw
       _b2012-10-15
995    _f11490-01
       _xachat
       _912756
       _cCMI
       _20
       _k13 ADA
       _o0
       _eSalle R
       _bCMI
001     8687
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