Algebra: Chapter 0

Paolo Aluffi, Florida State University, Tallahassee, FL.

• Preliminaries: Set theory and categoriesGroups, first encounterRings and modulesGroups, second encounterIrreducibility and factorization in integral domainsLinear algebraFieldsLinear algebra, repriseHomological algebraIndex

An obvious question: why another graduate algebra book? Aren't there all but too many already? Is there anything genuinely novel to be done when it comes to educating fledgling graduate students in this subject, given such an already well-populated and high-quality field? Well, the answer is yes. And the title of the book under review, Algebra: Chapter 0, is already a clue to what the author, Paolo Aluffi, is up to. In a perhaps Bourbakian sense, the prevailing motivation and objective is to present the subject at hand in a manner that pays proper due to relatively new foundations, making for a rather different orientation and flavor for what ensues. ...His treatment of these preliminaries is thorough as well as eminently accessible: Aluffi writes well, clearly and engagingly. This characterizes all of Algebra: Chapter 0, actually, and makes it easy to recommend the book enthusiastically even aside from the fact that I am a big fan of category theory to begin with."" —MAA Online""This self-contained introduction is suitable for a first sequence at the beginning graduate or upper undergraduate level. A distinguishing feature of the book is the early introduction of categories, used as a unifying theme."" SciTech Book News