Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available.
Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.
Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available.
Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of...
This volume has been curated from two sources: presentations from the Conference on Rings and Polynomials, Technische Universität Graz, Graz, Austria, July 19 -24, 2021, and papers...
The Making of Modern Law: Foreign, Comparative and International Law, 1600-1926, brings together foreign, comparative, and international titles in a single resource. Its...
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and...
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