This book will be particularly valuable to the American student because it covers material that is not available in any other textbooks or monographs. The subject of the book is not restricted to commutative algebra developed as a pure discipline for its own sake, nor is it aimed only at algebraic geometry where the intrinsic geometry of a general n-dimensional variety plays the central role. Instead, this book is developed around the vital theme that certain areas of both subjects are best understood together. This link between the two subjects, forged in the nineteenth century, built further by Krull and Zariski, remains as active as ever. In this book, the reader will find as the same time a leisurely and clear exposition of the basic definitions and results in both algebra and geometry, as well as an cxposition of the important recent progress fue to Quillen-Suslin, Evans-Eisenbud, Szpiro, Mohan Kumar and others. The ample exercises are another excellent feature. Professor Kunz has filled a longstanding need for an introduction to commutative algebra and algebraic geometry that emphasizes the concrete elementary nature of objects with which both subjects began.

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