Fröhlich, A. (Albrecht) 1916
Overview
Works:  34 works in 269 publications in 5 languages and 4,188 library holdings 

Genres:  Conference papers and proceedings Bibliography 
Roles:  Author, Editor 
Classifications:  QA247, 512.74 
Publication Timeline
.
Most widely held works by
A Fröhlich
Algebraic number theory by
A Fröhlich(
Book
)
80 editions published between 1967 and 2010 in English and Undetermined and held by 1,203 WorldCat member libraries worldwide
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical numbertheoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithmetic content. It will be indispensable for all practising and wouldbe algebraic number theorists
80 editions published between 1967 and 2010 in English and Undetermined and held by 1,203 WorldCat member libraries worldwide
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical numbertheoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithmetic content. It will be indispensable for all practising and wouldbe algebraic number theorists
Formal groups by
A Fröhlich(
Book
)
26 editions published between 1965 and 2007 in 3 languages and held by 468 WorldCat member libraries worldwide
26 editions published between 1965 and 2007 in 3 languages and held by 468 WorldCat member libraries worldwide
Galois module structure of algebraic integers by
A Fröhlich(
Book
)
21 editions published between 1983 and 2012 in English and German and held by 424 WorldCat member libraries worldwide
In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive takeoff point was the discovery of its connection with Artin Lfunctions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools
21 editions published between 1983 and 2012 in English and German and held by 424 WorldCat member libraries worldwide
In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive takeoff point was the discovery of its connection with Artin Lfunctions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools
Gauss sums and padic division algebras by
Colin J Bushnell(
Book
)
20 editions published between 1983 and 2008 in 3 languages and held by 393 WorldCat member libraries worldwide
20 editions published between 1983 and 2008 in 3 languages and held by 393 WorldCat member libraries worldwide
Algebraic number fields : (Lfunctions and Galois properties) : proceedings of a symposium by
A Fröhlich(
Book
)
25 editions published between 1976 and 1981 in English and Undetermined and held by 366 WorldCat member libraries worldwide
25 editions published between 1976 and 1981 in English and Undetermined and held by 366 WorldCat member libraries worldwide
Classgroups and Hermitian modules by
A Fröhlich(
Book
)
15 editions published between 1984 and 2012 in English and Italian and held by 312 WorldCat member libraries worldwide
These notes are an expanded and updated version of a course of lectures which I gave at King's College London during the summer term 1979. The main topic is the Hermitian classgroup of orders, and in particular of group rings. Most of this work is published here for the first time. The primary motivation came from the connection with the Galois module structure of rings of algebraic integers. The principal aim was to lay the theoretical basis for attacking what may be called the "converse problem" of Galois module structure theory: to express the symplectic local and global root numbers and conductors as algebraic invariants. A previous edition of these notes was circulated privately among a few collaborators. Based on this, and following a partial solution of the problem by the author, Ph. CassouNogues and M. Taylor succeeded in obtaining a complete solution. In a different direction J. Ritter published a paper, answering certain character theoretic questions raised in the earlier version. I myself disapprove of "secret circulation", but the pressure of other work led to a delay in publication; I hope this volume will make amends. One advantage of the delay is that the relevant recent work can be included. In a sense this is a companion volume to my recent SpringerErgebnisseBericht, where the Hermitian theory was not dealt with. Our approach is via "Homgroups", analogous to that followed in recent work on locally free classgroups
15 editions published between 1984 and 2012 in English and Italian and held by 312 WorldCat member libraries worldwide
These notes are an expanded and updated version of a course of lectures which I gave at King's College London during the summer term 1979. The main topic is the Hermitian classgroup of orders, and in particular of group rings. Most of this work is published here for the first time. The primary motivation came from the connection with the Galois module structure of rings of algebraic integers. The principal aim was to lay the theoretical basis for attacking what may be called the "converse problem" of Galois module structure theory: to express the symplectic local and global root numbers and conductors as algebraic invariants. A previous edition of these notes was circulated privately among a few collaborators. Based on this, and following a partial solution of the problem by the author, Ph. CassouNogues and M. Taylor succeeded in obtaining a complete solution. In a different direction J. Ritter published a paper, answering certain character theoretic questions raised in the earlier version. I myself disapprove of "secret circulation", but the pressure of other work led to a delay in publication; I hope this volume will make amends. One advantage of the delay is that the relevant recent work can be included. In a sense this is a companion volume to my recent SpringerErgebnisseBericht, where the Hermitian theory was not dealt with. Our approach is via "Homgroups", analogous to that followed in recent work on locally free classgroups
Central extensions, Galois groups, and ideal class groups of number fields by
A Fröhlich(
Book
)
14 editions published between 1980 and 1990 in English and held by 303 WorldCat member libraries worldwide
14 editions published between 1980 and 1990 in English and held by 303 WorldCat member libraries worldwide
Tame representations of local weil groups and of chain groups of local principal orders by
A Fröhlich(
Book
)
17 editions published in 1986 in English and German and held by 103 WorldCat member libraries worldwide
We begin by making clear the meaning of the term "tame". The higher ramifi cation groups, on the one hand, and the oneunits of chain groups, on the other, are to lie in the kernels of the respective representations considered. We shall establish a very natural and very well behaved relationship between representa tions of the two groups mentioned in the title, with all the right properties, and in particular functorial under base change and essentially preserving root numbers. All this will be done in full generality for all principal orders. The formal setup for this also throws new light on the nature of Gauss sums and in particular leads to a canonical closed formula for tame Galois Gauss sums. In many ways the "tame" and the "wild" theory have distinct features and distinct points of interest. The "wild" theory is much harder and  as far as it goes at present  technically rather complicated. On the "tame" side, once we have developed a number of new ideas, we get a complete comprehensive theory, from which technical difficulties have disappeared, and which has a naturality, and perhaps elegance, which seems rather rare in this gen, eral area. Among the principal new concepts we are introducing are those of "similarity" of represen tations in both contexts and that of the Galois algebra of a principalorder., One might expect that this Galois algebra will, also be of importance in the wild situation
17 editions published in 1986 in English and German and held by 103 WorldCat member libraries worldwide
We begin by making clear the meaning of the term "tame". The higher ramifi cation groups, on the one hand, and the oneunits of chain groups, on the other, are to lie in the kernels of the respective representations considered. We shall establish a very natural and very well behaved relationship between representa tions of the two groups mentioned in the title, with all the right properties, and in particular functorial under base change and essentially preserving root numbers. All this will be done in full generality for all principal orders. The formal setup for this also throws new light on the nature of Gauss sums and in particular leads to a canonical closed formula for tame Galois Gauss sums. In many ways the "tame" and the "wild" theory have distinct features and distinct points of interest. The "wild" theory is much harder and  as far as it goes at present  technically rather complicated. On the "tame" side, once we have developed a number of new ideas, we get a complete comprehensive theory, from which technical difficulties have disappeared, and which has a naturality, and perhaps elegance, which seems rather rare in this gen, eral area. Among the principal new concepts we are introducing are those of "similarity" of represen tations in both contexts and that of the Galois algebra of a principalorder., One might expect that this Galois algebra will, also be of importance in the wild situation
Bibliographie cartographique internationale, 19461947 by
M Foncin(
Book
)
14 editions published between 1949 and 1972 in French and Undetermined and held by 17 WorldCat member libraries worldwide
14 editions published between 1949 and 1972 in French and Undetermined and held by 17 WorldCat member libraries worldwide
Sekundäre basilare impression bei calcipenischer osteopathie klinischröntgenologische untersuchungen by
A Fröhlich(
)
3 editions published in 1969 in German and held by 11 WorldCat member libraries worldwide
3 editions published in 1969 in German and held by 11 WorldCat member libraries worldwide
Gauss'sche Summen by
A Fröhlich(
Book
)
2 editions published between 1983 and 1984 in German and held by 7 WorldCat member libraries worldwide
2 editions published between 1983 and 1984 in German and held by 7 WorldCat member libraries worldwide
Gauss'sche Summen by
A Fröhlich(
Book
)
2 editions published between 1983 and 1984 in German and held by 7 WorldCat member libraries worldwide
2 editions published between 1983 and 1984 in German and held by 7 WorldCat member libraries worldwide
Gauss'sche Summen : nach Vorlesungen gehalten in Köln 1982 u. Cambridge, 1983 by
A Fröhlich(
Book
)
3 editions published in 1983 in German and Undetermined and held by 6 WorldCat member libraries worldwide
3 editions published in 1983 in German and Undetermined and held by 6 WorldCat member libraries worldwide
Algebraičeskaja teorija čisel(
Book
)
2 editions published in 1969 in Russian and held by 5 WorldCat member libraries worldwide
2 editions published in 1969 in Russian and held by 5 WorldCat member libraries worldwide
Gauss'sche Summen : nach Vorlesungen von A. Fröhlich gehalten in Köln 1982 u. Cambridge 1983 by
A Fröhlich(
Book
)
2 editions published in 1983 in German and Undetermined and held by 4 WorldCat member libraries worldwide
2 editions published in 1983 in German and Undetermined and held by 4 WorldCat member libraries worldwide
The rational characterization of certain sets of relatively Abelian extensions by
A Fröhlich(
Book
)
1 edition published in 1959 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1959 in English and held by 3 WorldCat member libraries worldwide
Gauss'sche Summen by
A Fröhlich(
Book
)
2 editions published in 1983 in German and held by 2 WorldCat member libraries worldwide
2 editions published in 1983 in German and held by 2 WorldCat member libraries worldwide
Effectice procedures in field theory by
A Fröhlich(
Book
)
2 editions published in 1956 in Undetermined and English and held by 2 WorldCat member libraries worldwide
2 editions published in 1956 in Undetermined and English and held by 2 WorldCat member libraries worldwide
Sectentum und Separatismus im jetzigen kirchligne Leben der evangelischen Befölkerung ElsassLothringens by
A Fröhlich(
Book
)
1 edition published in 1889 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 1889 in German and held by 2 WorldCat member libraries worldwide
Algebraičeskaâ teoriâ čisel(
Book
)
2 editions published in 1969 in Russian and held by 2 WorldCat member libraries worldwide
2 editions published in 1969 in Russian and held by 2 WorldCat member libraries worldwide
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Related Identities
 London Mathematical Society Other Publisher Author Editor Publishing director
 Cassels, J. W. S. (John William Scott) Author Editor
 International Mathematical Union Other
 Bushnell, Colin J. (Colin John) 1947 Author
 Taylor, Martin (Martin J.)
 SpringerLink (Service en ligne)
 Taylor, M. J.
 Foncin, M. Publishing director Author Editor
 Symposium on LFunctions and Galois Properties of Algebraic Number Fields (1975, Durham)
 Sommer, P.
Useful Links
Associated Subjects
Algebra Algebra, Abstract Algebraic fields Algebraic number theory Algebraic topology Class field theory Class groups (Mathematics) Division algebras Field extensions (Mathematics) Field theory (Physics) Finite fields (Algebra) Finite groups Formal groups Galois modules (Algebra) Galois theory Gaussian sums Geometry, Algebraic Group theory Integral representations Ktheory Lfunctions Maps Mathematics Modules (Algebra) Number theory Representations of groups Rings (Algebra) Weil group
Alternative Names
Albrecht Fröhlich britischer Mathematiker
Albrecht Fröhlich British mathematician
Albrecht Fröhlich britisk matematikar
Albrecht Fröhlich britisk matematiker
Albrecht Fröhlich Brits wiskundige (19162001)
Albrecht Fröhlich brittisk matematiker
Albrecht Fröhlich matemático británico
Albrecht Fröhlich mathématicien britannique
Frëlih, A.
Froehlich, A. 19162001
Fröhlich, A.
Fröhlich, A. 19162001
Fröhlich, Albrecht
Fröhlich, Albrecht 1916
Fröhlich, Albrecht 19162001
Fröhlich, Ali 19162001
Фрёлих, А.
阿爾佈雷希特·弗勒利希
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