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Indigo An Introduction to Algebraic Number Theory: Distribution of Units Modulo An Integral Ideal | Erin Mills Town Centre
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This book offers a clear, self-contained introduction to algebraic number theory, guiding readers from foundational concepts to a largely unexplored research topic: the distribution of units in algebraic number fields modulo integral ideals.The text is organized in two complementary parts. Part I develops the theory systematically, beginning with elementary number theory and progressing through algebraic integers, ideals, lattices, norms, ramification, discriminants, cyclotomic fields, and the Chebotarev theorem. It culminates in a substantial and original treatment of the distribution of units, including explicit computations, density results, and detailed examples across a range of number fields.Part II provides a concise and accessible introduction to abstract algebra, covering groups, rings, fields, Galois theory, and Kummer extensions. This ensures that the book is fully self-contained and suitable for readers encountering the subject for the first time.Emphasizing a global perspective in algebraic number theory, the book reflects a renewed modern interest in global arithmetic structures. Numerous examples, complete proofs, and carefully designed exercises support a gradual progression from basic theory to advanced topics.Suitable for advanced undergraduate and graduate courses, this book also serves as a bridge to current research, equipping readers with the tools and insight needed to explore open problems in number theory.
This book offers a clear, self-contained introduction to algebraic number theory, guiding readers from foundational concepts to a largely unexplored research topic: the distribution of units in algebraic number fields modulo integral ideals.The text is organized in two complementary parts. Part I develops the theory systematically, beginning with elementary number theory and progressing through algebraic integers, ideals, lattices, norms, ramification, discriminants, cyclotomic fields, and the Chebotarev theorem. It culminates in a substantial and original treatment of the distribution of units, including explicit computations, density results, and detailed examples across a range of number fields.Part II provides a concise and accessible introduction to abstract algebra, covering groups, rings, fields, Galois theory, and Kummer extensions. This ensures that the book is fully self-contained and suitable for readers encountering the subject for the first time.Emphasizing a global perspective in algebraic number theory, the book reflects a renewed modern interest in global arithmetic structures. Numerous examples, complete proofs, and carefully designed exercises support a gradual progression from basic theory to advanced topics.Suitable for advanced undergraduate and graduate courses, this book also serves as a bridge to current research, equipping readers with the tools and insight needed to explore open problems in number theory.
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