Aron Simis

ISBNs: 3111078450, 3111078841, 3110616971, 9783110616972,
9783111078458, 9783111078847, 9783111078786, 978-3110616972,
978-3111078458, 978-3111078847, 978-3111078786, B0C8FWTFGT

English | 2024 | Original PDF, EPUB | 370 Pages

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).