Franz Halter-Koch – författare
1 177 kr
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The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume.
The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory.
Key features:
• A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis.• Several of the topics both in the number field and in the function field case were not presented before in this context.• Despite presenting many advanced topics, the text is easily readable.
Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of “Ideal Systems” (Marcel Dekker,1998), “Quadratic Irrationals” (CRC, 2013), and a co-author of “Non-Unique Factorizations” (CRC 2006).
1 177 kr
Läs direkt efter köp
The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume.
The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory.
Key features:
• A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis.• Several of the topics both in the number field and in the function field case were not presented before in this context.• Despite presenting many advanced topics, the text is easily readable.
Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of “Ideal Systems” (Marcel Dekker,1998), “Quadratic Irrationals” (CRC, 2013), and a co-author of “Non-Unique Factorizations” (CRC 2006).
1 244 kr
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The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras.
While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020).
The main features of the book are:
A detailed study of Pontrjagin’s dualtiy theorem.
A thorough presentation of the cohomology of profinite groups.
A introduction to simple algebras.
An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language.
The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse.
The study of holomorphy domains and their relevance for class field theory.
Simple classical proofs of the functional equation for L functions both for number fields and function fields.
A self-contained presentation of the theorems of representation theory needed for Artin L functions.
Application of Artin L functions for arithmetical results.
1 244 kr
Läs direkt efter köp
The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras.
While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020).
The main features of the book are:
A detailed study of Pontrjagin’s dualtiy theorem.
A thorough presentation of the cohomology of profinite groups.
A introduction to simple algebras.
An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language.
The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse.
The study of holomorphy domains and their relevance for class field theory.
Simple classical proofs of the functional equation for L functions both for number fields and function fields.
A self-contained presentation of the theorems of representation theory needed for Artin L functions.
Application of Artin L functions for arithmetical results.
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Ideal Theory of Commutative Rings and Monoids
811 kr
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1 029 kr
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This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Prüfer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.