Graduate Algebra: Commutative View (73) - Rilegato

Rowen, Louis Halle

Rilegato

ISBN 10: 0821805703 ISBN 13: 9780821805701

Casa editrice: Amer Mathematical Society, 2006

Riassunto

This book is an expanded text for a graduate course in commutative algebra, focusing on the algebraic underpinnings of algebraic geometry and of number theory. Accordingly, the theory of affine algebras is featured, treated both directly and via the theory of Noetherian and Artinian modules, and the theory of graded algebras is included to provide the foundation for projective varieties. Major topics include the theory of modules over a principal ideal domain, and its applications to matrix theory (including the Jordan decomposition), the Galois theory of field extensions, transcendence degree, the prime spectrum of an algebra, localization, and the classical theory of Noetherian and Artinian rings. Later chapters include some algebraic theory of elliptic curves (featuring the Mordell-Weil theorem) and valuation theory, including local fields. One feature of the book is an extension of the text through a series of appendices. This permits the inclusion of more advanced material, such as transcendental field extensions, the discriminant and resultant, the theory of Dedekind domains, and basic theorems of rings of algebraic integers. An extended appendix on derivations includes the Jacobian conjecture and Makar-Limanov's theory of locally nilpotent derivations. Grobner bases can be found in another appendix. Exercises provide a further extension of the text. The book can be used both as a textbook and as a reference source.

Su questo libro

Product Description:

Book by Louis Halle Rowen

Su questa edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2006
• ISBN 10: 0821805703
• ISBN 13: 9780821805701
• Rilegatura: Copertina rigida
• Numero di pagine: 399