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On a Tower of Fields Related to On_p

Jeeninga, M. (2015) On a Tower of Fields Related to On_p. Master's Thesis / Essay, Mathematics.

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Abstract

We study an Artin-Schreier tower of fields over GF(p), for p a prime. We will show that the extensions in this tower are made by adjoining a root of the first irreducible polynomial of degree p with respect to the reverse lexicographical ordering. This generalizes a tower of fields studied by J.H. Conway and H.W. Lenstra, Jr. in the 70s. Among other things, we give an algorithm to compute the minimal polynomials of generators in this tower and we will solve a problem posed by Lenstra in "Nim Multiplication'' (1978) for the case p=2, and prove a generalization for p>2.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 08:08
Last Modified: 15 Feb 2018 08:08
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/13312

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