Commutative Algebra / Aron Simis.

Format:

Book

Author/Creator:

Simis, Aron, Author.

Series:

De Gruyter Textbook

Language:

English

Physical Description:

1 online resource (XX, 350 p.)

Edition:

2nd, revised Edition

Place of Publication:

Berlin ; Boston : De Gruyter, [2023]

Language Note:

In English.

Summary:

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).

Contents:

Frontmatter

Thanks

Foreword

Foreword to the second edition

Contents

Part I

1 Basic introductory theory

2 Main tools

3 Overview of module theory

4 Derivations, differentials and Jacobian ideals

Part II

5 Basic advanced theory

6 Homological methods

7 Graded structures

Bibliography

Index

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Aug 2023)

ISBN:

9783111078786

3111078787