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Algebra : [Book] : an approach via module theory / William A. Adkins, Steven H. Weintraub.

By: Contributor(s): Material type: TextTextSeries: Graduate texts in mathematics ; 136Publication details: New York : Springer-Verlag, c1992.Description: x, 526 pages : illustrations ; 25 cmISBN:
  • 3540978399(Berlin)
  • 0387978399
Subject(s): DDC classification:
  • 512.4 20
Other classification:
  • 512.4
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 generalizaƯ tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books Books Junaid Zaidi Library, COMSATS University Islamabad Ground Floor 512.4 ADK-A (Browse shelf(Opens below)) Available 55903
Total holds: 0

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 generalizaƯ tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.

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