Buch, Englisch, Band 73, 399 Seiten, Format (B × H): 185 mm x 263 mm, Gewicht: 944 g
Buch, Englisch, Band 73, 399 Seiten, Format (B × H): 185 mm x 263 mm, Gewicht: 944 g
Reihe: Graduate Studies in Mathematics
ISBN: 978-0-8218-0570-1
Verlag: American Mathematical Society
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.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Algebra Elementare Algebra
- Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
- Mathematik | Informatik Mathematik Algebra Zahlentheorie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
- Naturwissenschaften Physik Quantenphysik
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
