FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 4, PAGES 1257-1261
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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Last modified: February 13, 2001