Integral Closure of Ideals, Rings, and Modules


Book Description

Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.










Dissertation Abstracts


Book Description

Abstracts of dissertations and monographs in microform.




Notices of the American Mathematical Society


Book Description

Contains articles of significant interest to mathematicians, including reports on current mathematical research.













Valued Fields


Book Description

Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.




The Geometry of Schemes


Book Description

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.