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Table of contents (20 chapters)
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Front Matter
Keywords
About this book
The laws of composition include addition and multiplication of numbers or func tions. These are the basic operations of algebra. One can generalize these operations to groups where there is just one law. The theory of this book was started in 1800 by Gauss, when he solved the 2000 year-old Greek problem about constructing regular n-gons by ruler and compass. The theory was further developed by Abel and Galois. After years of development the theory was put in the present form by E. Noether and E. Artin in 1930. At that time it was called modern algebra and concentrated on the abstract exposition of the theory. Nowadays there are too many examples to go into their details. I think the student should study the proofs of the theorems and not spend time looking for solutions to tricky exercises. The exercises are designed to clarify the theory. In algebra there are four basic structures; groups, rings, fields and modules. We present the theory of these basic structures. Hopefully this will give a good introduc tion to modern algebra. I have assumed as background that the reader has learned linear algebra over the real numbers but this is not necessary.
Authors and Affiliations
About the author
Prof. Georg Kempf lehrt an der Johns Hopkins University; Baltimore, Maryland, USA.
Bibliographic Information
Book Title: Algebraic Structures
Authors: George R. Kempf
DOI: https://doi.org/10.1007/978-3-322-80278-1
Publisher: Vieweg+Teubner Verlag Wiesbaden
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eBook Packages: Springer Book Archive
Copyright Information: Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1995
Softcover ISBN: 978-3-528-06583-6Published: 01 January 1995
eBook ISBN: 978-3-322-80278-1Published: 06 December 2012
Edition Number: 1
Number of Pages: IX, 166
Topics: Algebra