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