Ideals, Varieties, and Algorithms (5th Edition)
by David A. Cox, John Little, Donal O'Shea · Springer (Undergraduate Texts in Mathematics)
Undergraduate text on multivariable polynomial rings: monomial orders, the multivariable division algorithm, Groebner bases and Buchberger's algorithm, the Hilbert basis theorem, elimination theory, and the ideal-variety correspondence, with computer algebra exercises. Chapters 1-2 are the definitive accessible treatment of ideals in k[x1,...,xn] and the multivariable division algorithm.
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