This book provides the traditional role of exercises in a course to provide more-or-less routine applications of the main results, for the student's edification and also as possible material for examinations. It discusses Noetherian rings and prime ideals for algebraic geometry.
Some of the most famous questions in mathematical history have involved equations with coefficients in Z, the set of integers. This book deals with their solutions, which are achieved with an economy of effort through the process of abstraction. It presents both results and their underlying ideas.
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