Cambridge University Press Undergraduate Commutative Algebra: 29 (London Mathematical Society Student Texts, Series Number 29)

Product Description Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world. Review 'It gives a fresh picture of the subject for a new generation of students.' P. Scnezel, Zentralblatt fur Mathematik'The author takes care to explain the geometric and number theoretic meaning of the algebraic methods and results presented. This makes the book perhaps more demanding, but surely much more interesting than the standard ones.' European Mathematical Society Newsletter'Besides the usual topics … there are some welcome geometrical illustrations, as well as some homespun philosophy.' Mathematica Book Description For those looking for an introduction to the area of commutative algebra, this book opens all the right doors and provides a clarity of understanding that all will welcome.