Author: Irving Reiner
Publisher: American Mathematical Soc.
ISBN: 0821816764
Category : Mathematics
Languages : en
Pages : 50
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Book Description
The aim of the lectures is to provide an introduction to recent developments in the theory of class groups and Picard groups. The techniques employed come from the three main areas: algebraic number theory, representation theory of algebras and orders, and algebraic $K$-theory.
Author: K.W. Roggenkamp
Publisher: Birkhäuser
ISBN: 303488611X
Category : Mathematics
Languages : en
Pages : 215
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Book Description
The first part of the book centers around the isomorphism problem for finite groups; i.e. which properties of the finite group G can be determined by the integral group ring ZZG ? The authors have tried to present the results more or less selfcontained and in as much generality as possible concerning the ring of coefficients. In the first section, the class sum correspondence and some related results are derived. This part is the proof of the subgroup rigidity theorem (Scott - Roggenkamp; Weiss) which says that a finite subgroup of the p-adic integral group ring of a finite p-group is conjugate to a subgroup of the finite group. A counterexample to the conjecture of Zassenhaus that group basis are rationally conjugate, is presented in the semilocal situation (Scott - Roggenkamp). To this end, an extended version of Clifford theory for p-adic integral group rings is presented. Moreover, several examples are given to demonstrate the complexity of the isomorphism problem. The second part of the book is concerned with various aspects of the structure of rings of integers as Galois modules. It begins with a brief overview of major results in the area; thereafter the majority of the text focuses on the use of the theory of Hopf algebras. It begins with a thorough and detailed treatment of the required foundational material and concludes with new and interesting applications to cyclotomic theory and to elliptic curves with complex multiplication. Examples are used throughout both for motivation, and also to illustrate new ideas.
Author: J. S. Hsia
Publisher: Springer
ISBN: 3540378189
Category : Mathematics
Languages : en
Pages : 235
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Author: Klaus W. Roggenkamp
Publisher: Springer
ISBN: 3540387897
Category : Mathematics
Languages : en
Pages : 490
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 160
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Book Description
Author: Bernard R. McDonald
Publisher: CRC Press
ISBN: 1000110613
Category : Mathematics
Languages : en
Pages : 561
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Book Description
This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Author: Bruce A. Magurn
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 836
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Book Description
Author: F. van Oystaeyen
Publisher: Springer
ISBN: 354039057X
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9400959885
Category : Mathematics
Languages : en
Pages : 540
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Book Description
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
