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" $a$_{1}x^{l1} + ¼ + a_{s}x^{ls}
($a$_{i} Î K, $$l_{i} Î **Q**,
$$l
_{i} ³ 0).
Consider the set of elements $S$ closed under
multiplication and generated by the elements $x1/m$,
$1\; +\; x1/m+$¼ + x^{k/m}
($m$ and $k$ vary).
We prove that the ring $RS$-1 is
a principal ideal ring.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k00/k004/k00422h.htm

Last modified: February 13, 2001