On a proposition of Samuel and 2-stage Euclidean algorithm in global fields

Ching An Chen; Ming Guang Leu

doi:10.1016/j.jnt.2012.07.009

On a proposition of Samuel and 2-stage Euclidean algorithm in global fields

Ching An Chen
, Ming Guang Leu

Department of Mathematics

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

3 Scopus citations

Abstract

In this article we will extend a proposition of P. Samuel, which is related to the concept of Euclidean domains, to a class of commutative rings with zero divisors. Also we will derive an analog of Samuel's proposition for the concept of 2-stage Euclidean rings, and give application to global fields.

Original language	English
Pages (from-to)	215-225
Number of pages	11
Journal	Journal of Number Theory
Volume	133
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2012.07.009
State	Published - Jan 2013

Keywords

2-Stage Euclidean ring
Euclidean ring
Global field
Number field
Order of number field
Quasi-Euclidean ring
Ring of S-integers
ω-Stage Euclidean ring

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10.1016/j.jnt.2012.07.009

Cite this

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abstract = "In this article we will extend a proposition of P. Samuel, which is related to the concept of Euclidean domains, to a class of commutative rings with zero divisors. Also we will derive an analog of Samuel's proposition for the concept of 2-stage Euclidean rings, and give application to global fields.",

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AU - Leu, Ming Guang

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AB - In this article we will extend a proposition of P. Samuel, which is related to the concept of Euclidean domains, to a class of commutative rings with zero divisors. Also we will derive an analog of Samuel's proposition for the concept of 2-stage Euclidean rings, and give application to global fields.

KW - 2-Stage Euclidean ring

KW - Euclidean ring

KW - Global field

KW - Number field

KW - Order of number field

KW - Quasi-Euclidean ring

KW - Ring of S-integers

KW - ω-Stage Euclidean ring

UR - https://www.scopus.com/pages/publications/84867459349

U2 - 10.1016/j.jnt.2012.07.009

DO - 10.1016/j.jnt.2012.07.009

M3 - 期刊論文

AN - SCOPUS:84867459349

SN - 0022-314X

VL - 133

SP - 215

EP - 225

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

On a proposition of Samuel and 2-stage Euclidean algorithm in global fields

Abstract

Keywords

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