Introduction to Algebra

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Oxford University Press, 1998 - Mathematics - 295 pages
2 Reviews
This book is an undergraduate textbook on abstract algebra, beginning with the theories of rings and groups. As this is the first really abstract material students need, the pace here is gentle, and the basic concepts of subring, homomorphism, ideal, etc are developed in detail. Later, as students gain confidence with abstractions, they are led to further developments in group and ring theory (simple groups and extensions, Noetherian rings, and outline of universal algebra, lattices andcategories) and to applications such as Galois theory and coding theory. There is also a chapter outlining the construction of the number systems from scratch and proving in three different ways that trascendental numbers exist.
 

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Contents

Introduction
1
Rings
25
Groups
65
Vector spaces
103
Modules
135
The number systems
159
Further topics
181
Applications
235
Further reading
269
Index
287
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About the author (1998)

Peter J. Cameron is a Professor of Mathematics at Queen Mary and Westfield College, London.

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