# Advanced Algebra

## Along with a companion volume Basic Algebra

Part of the Cornerstones book series (COR)

Part of the Cornerstones book series (COR)

*Basic Algebra* and *Advanced Algebra* systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.

Key topics and features of *Advanced Algebra*:

*Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in *Basic Algebra*

*Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry

*Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications

*Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis

*Book carries on two prominent themes recurring in *Basic Algebra*: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry

*Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems

*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics

*Advanced Algebra* presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in *Basic Algebra*.

Algebra Group theory Homological algebra algebraic geometry algebraic number theory finite field number theory ring theory

- DOI https://doi.org/10.1007/978-0-8176-4613-4
- Copyright Information Birkhäuser Boston 2008
- Publisher Name Birkhäuser, Boston, MA
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-8176-4522-9
- Online ISBN 978-0-8176-4613-4
- Series Print ISSN 2197-182X
- Series Online ISSN 2197-1838
- About this book