Journal ArticleDOI
On the construction of division chains in algebraic number rings,with applications to SL2
George Cooke,Peter J. Weinberger +1 more
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This article is published in Communications in Algebra.The article was published on 1975-01-01. It has received 77 citations till now. The article focuses on the topics: Division (mathematics) & Algebraic number.read more
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Introduction to Arithmetic Groups
TL;DR: A good introduction to the study of arithmetic subgroups of semisimple Lie groups can be found in this article, where the authors provide primers on lattice subgroups, arithmetic groups, real rank and Q-rank, ergodic theory, unitary representations, amenability, and quasi-isometries.
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Bounded generation and Kazhdan’s property $(T)$
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Artin's primitive root conjecture -a survey -
TL;DR: A survey of the literature on this topic emphasizing the Artin primitive root conjecture (1927) and the contributions in the survey on `elliptic Artin' are due to Alina Cojocaru.
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On Artin's conjecture and Euclid's algorithm in global fields
TL;DR: In this paper, the authors considered a generalization of Artin's conjecture on primes with prescribed primitive roots and provided a necessary and sufficient condition for the conjectural density of certain sets of primes to be non-zero.
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Journal Article
On Artin's conjecture.
TL;DR: The problem of determining the prime numbers p for which a given number a is a primitive root, modulo JP, was first considered by Gauss in the Disquisitiones Arithmeticae that is devoted to the periodie deeimal expansions of fraetions with denominator p.
Journal Article
A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.
TL;DR: In this paper, the class number of a ring of algebraic integers is defined as the number of classes of ideals in the ideal class group of the ring R such that R is a UFD if and only if h = 1.