FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 4, PAGES 1257-1261

A construction of principal ideal rings

Yu. V. Kuzmin

Abstract

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Let $K$ be an algebraic number field, and let $R$ be the ring that consists of ``polynomials'' $a_1x^{\lambda_1} + \ldots + a_s x^{\lambda_s}$ ($a_i \in K$, $\lambda_i \in \mathbb Q$, $\lambda_i \geq 0$). Consider the set of elements $S$ closed under multiplication and generated by the elements $x^{1/m}$, $1 + x^{1/m} + \ldots + x^{k/m}$ ($m$ and $k$ vary). We prove that the ring $RS^{-1}$ is a principal ideal ring.

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