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^l₁ + ¼ + a_sx^l_s ($a$_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.

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Last modified: February 13, 2001