Abstract

AbstractIn this chapter we develop basic algebraic notions and facts to the extent needed for the applications in this book. Equally important are the examples for such structures from number theory. At the center of attention are basic facts from group theory, especially about cyclic groups, which are central in the analysis of the deterministic primality test. We discuss (commutative) rings (with 1), with the central example being ℤ m . Finally, we develop the basic facts about finite fields, in particular we establish that in finite fields the multiplicative group is cyclic.KeywordsGroup OperationPrime NumberCyclic GroupFinite FieldBinary OperationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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