Growth Results and Euclidean Ideals

Details Growth Results and Euclidean Ideals Growth Results and Euclidean Ideals

2010-08-14

arxiv.org/abs/1008.2479v1

Mathematics

Number Theory

16 pages

Scientific paper

Lenstra's concept of Euclidean ideals generalizes the Euclidean algorithm; a domain with a Euclidean ideal has cyclic class group, while a domain with a Euclidean algorithm has trivial class group. This paper generalizes Harper's variation of Motzkin's lemma to Lenstra's concept of Euclidean ideals and then uses the large sieve to obtain growth results. It concludes that if a certain set of primes is large enough, then the ring of integers of a number field with cyclic class group has a Euclidean ideal.

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