A sufficient condition of Euclidean rings given by polynomial optimization over a box

Shenggui Zhang

doi:10.3934/naco.2014.4.93

Article Contents

2014, Volume 4, Issue 2: 93-101. Doi: 10.3934/naco.2014.4.93

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A sufficient condition of Euclidean rings given by polynomial optimization over a box

Shenggui Zhang^1,

1.
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007

Received: June 2013

Revised: December 2013

Published: May 2014

Abstract / Introduction Related Papers Cited by

Abstract

A sufficient condition of Euclidean rings is given by polynomial optimization. Then, through computation, we give all norm-Euclidean square number fields, four examples of norm-Euclidean cubic number fields and two examples of norm-Euclidean cyclotomic fields, with the absolute of a norm less than 1 over the corresponding box, respectively.

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Mathematics Subject Classification: Primary: 13F07; Secondary: 90C26.

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