The euclidean algorithm for number fields and primitive roots

M. R. Murty; Kathleen L. Petersen

doi:10.1090/S0002-9939-2012-11327-9

The euclidean algorithm for number fields and primitive roots

M. R. Murty, Kathleen L. Petersen

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let K be a number field with unit rank at least four, containing a subfield M such that K/M is Galois of degree at least four. We show that the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann Hypothesis for Dedekind zeta functions. We prove this unconditionally.

Original language	English (US)
Pages (from-to)	181-190
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-2012-11327-9
State	Published - 2012
Externally published	Yes

Keywords

Euclidean algorithm
Large sieve
Primitive roots

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10.1090/S0002-9939-2012-11327-9

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abstract = "Let K be a number field with unit rank at least four, containing a subfield M such that K/M is Galois of degree at least four. We show that the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann Hypothesis for Dedekind zeta functions. We prove this unconditionally.",

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AU - Murty, M. R.

AU - Petersen, Kathleen L.

PY - 2012

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AB - Let K be a number field with unit rank at least four, containing a subfield M such that K/M is Galois of degree at least four. We show that the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann Hypothesis for Dedekind zeta functions. We prove this unconditionally.

KW - Euclidean algorithm

KW - Large sieve

KW - Primitive roots

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

The euclidean algorithm for number fields and primitive roots

Abstract

Keywords

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