Algebra : an approach via module theory
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TextLanguage: English Series: Graduate texts in mathematics ; 136Publication details: Heidelberg : Springer, 1992. Description: x, 526p. : ill. ; 25 cmISBN: 9781493999125Subject(s): Algebra | Modules (Algebra) | Quadratic form | HomomorphismDDC classification: 512.55 Online resources: Table of contents | Reviews Summary: This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Book
|
NISER LIBRARY | 512.55 ADK-A (Browse shelf(Opens below)) | Available | 25254 |
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| 512.547.4 BOR-R Representations of the infinite symmetric group | 512.547.4 ROG-A Automorphic representations of unitary groups in three variables | 512.548 PAT-G Groupoids, inverse semigroups, and their operator algebras | 512.55 ADK-A Algebra : an approach via module theory | 512.55 AND-R Rings and categories of modules | 512.55 AND-R Course in the theory of groups (a) | 512.55 BOR-N Nilpotentorbits, primitive ideals, and characteristic classes : a geometric perspective in ring theory |
Includes bibliographical references (p. [510]) and indexes.
This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.
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