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Synopsis
An Introduction to Commutative Algebra and Number Theory is an elementary introduction to these subjects. Beginning with a concise review of groups, rings and fields, the author presents topics in algebra from a distinctly number-theoretic perspective and sprinkles number theory results throughout his presentation. The topics in algebra include polynomial rings, UFD, PID, and Euclidean domains; and field extensions, modules, and Dedekind domains. In the section on number theory, in addition to covering elementary congruence results, the laws of quadratic reciprocity and basics of algebraic number fields, this book gives glimpses into some deeper aspects of the subject. These include Warning's and Chevally's theorems in the finite field sections, and many results of additive number theory, such as the derivation of LaGrange's four-square theorem from Minkowski's result in the geometry of numbers. With addition of remarks and comments and with references in the bibliography, the author stimulates readers to explore the subject beyond the scope of this book.
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About the Author
Sukumar Das Adhikari.: The Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad, India
"About this title" may belong to another edition of this title.
- PublisherNarosa Pub House
- Publication date1999
- ISBN 10 8173193045
- ISBN 13 9788173193040
- BindingHardcover
- LanguageEnglish
- Number of pages166
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An Introduction to Commutative Algebra and Number Theory
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Narosa Publishing House, 1999
ISBN 10: 8173193045
ISBN 13: 9788173193040
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An Introduction to Commutative Algebra and Number Theory
Published by
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ISBN 10: 8173193045
ISBN 13: 9788173193040
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