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2014 | OriginalPaper | Chapter

1. Rings, Algebras and Modules

Author : Alexander Zimmermann

Published in: Representation Theory

Publisher: Springer International Publishing

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Abstract

In this first chapter we provide the necessary facts in elementary module theory, we define the concept of a representation, and give elementary applications to representations of groups. We also provide a short introduction to the basic concepts leading to homological algebra, as far as it is necessary to understand the elementary modular representation theory of finite groups as it is developed in Chap. 2. We restrict ourselves to a selection of those properties that are going to be used in the sequel and avoid developing the theory in directions which are not explicitly used in later chapters. This way the book remains completely self-contained, without being encyclopedic, and the choice will also allows us to fix a coherent notation throughout.

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next chapter Modular Representations of Finite Groups
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Metadata
Title
Rings, Algebras and Modules
Author
Alexander Zimmermann
Copyright Year
2014
Book
Representation Theory

Print ISBN: 978-3-319-07967-7

Electronic ISBN: 978-3-319-07968-4

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-07968-4_1

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