Commutative Algebra

The primary audience for this book is students and the young  researchers interested in the core of the discipline. Commutative  algebra is by and large a self-contained discipline, which makes it  quite dry for the beginner with a basic training in elementary algebra  and calculus. 

A stable mathematical discipline such  as this enshrines a vital number of topics to be learned at an early  stage, more or less universally accepted and practiced. Naturally,  authors tend to turn these topics into an increasingly short and elegant  list of basic facts of the theory. So, the shorter the better. However,  there is a subtle watershed between elegance and usefulness, especially  if the target is the beginner. From my experience throughout years of  teaching, elegance and terseness do not do it, except much later in the  carrier. To become useful, the material ought to carry quite a bit of  motivation through justification and usefulness pointers. 

On  the other hand, it is difficult to contemplate these teaching devices  in the writing of a short book. I have divided the material in three  parts. starting with more elementary sections, then carrying an  intermezzo on more difficult themes to make up for a smooth crescendo  with additional tools and, finally, the more advanced part, versing on a  reasonable chunk of present-day steering of commutative algebra. 

Historic  notes at the end of each chapter provide insight into the original  sources and background information on a particular subject or theorem. 

Exercises  are provided and propose problems that apply the theory to solve  concrete questions (yes, with concrete polynomials, and so forth).