Graduate Algebra by Leonard Evens - PDF
About this book :-
This graduate level textbook focuses on commutative algebra , with applications to algebraic geometry and number theory. In this book we shall study some elementary properties of Krull rings and factorial rings, regular rings (local and factorial), and descent methods (Galoisia theory and Applications). The book is structured into three main parts:
Modules: Covers the theory of modules over commutative rings, including finitely generated modules, simple modules, and composition series.
Affine Algebras and Noetherian Rings: Explores Galois theory of fields, affine algebras, transcendence degree, Krull dimension, localization, and the prime spectrum of a ring.
Applications to Geometry and Number Theory: Discusses algebraic foundations of geometry, Diophantine equations, elliptic curves, valuation theory, and local fields.
The book also includes appendices covering advanced topics like transcendental field extensions and Gröbner bases. Exercises are provided to reinforce the material, making it suitable for both classroom use and self-study. It serves as a valuable resource for graduate students and researchers interested in algebra, geometry, and number theory.
Book Detail :-
Title:
Graduate Algebra by Leonard Evens - PDF
Publisher:
Northwestern University
Year:
1999
Pages:
160
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
Leonard Evens
is a mathematician and professor from Northwestern University, Evanston, Illinois, United States. He is known for his work in algebra, especially in a subject called group cohomology. He wrote a book called The Cohomology of Groups, which explains this advanced topic in a clear and modern way. He is also known for being a good teacher and has shared a helpful free textbook on linear algebra.
Book Contents :-
1. GROUPS
2. GROUP ACTIONS ON SETS
3. NORMAL SERIES
4. RING THEORY
5. MODULES
6. HOM AND TENSOR
7. FIELD THEORY
8. ALOIS THEOR
9. APPLICATIONS OF GALOIS THEORY
10. INFINITE EXTENSIONS
11. INFINITE EXTENSIONS
12. MULTILINEAR ALGEBRA
13. MORE RING THEORY
14. LOCALILAZATION
15. INTEGRAL EXTENSIONS
16. NONCOMMUTATIVE RINGS
17. SIMPLE RINGS
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