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<p>In this paper, we consider continued fractions with elements from some special algebras. In absence of commutativity under multiplication, the study of properties of continued fractions is significantly complicated. For such fractions, some concepts related to classical continued fractions need to be modified. At the same time, generalized continued fractions studied in the paper meet many properties of the classical continued fractions. In particular, values of the residuals are calculated using similar formulas. The most complete results are obtained for continued fractions on the set of quaternions. Bibliography: 20 titles.</p>

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ON REPRESENTATION OF ELEMENTS OF SOME SPECIAL ALGEBRAS BY CONTINUED FRACTIONS

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • S. M. Khryaschev

摘要

In this paper, we consider continued fractions with elements from some special algebras. In absence of commutativity under multiplication, the study of properties of continued fractions is significantly complicated. For such fractions, some concepts related to classical continued fractions need to be modified. At the same time, generalized continued fractions studied in the paper meet many properties of the classical continued fractions. In particular, values of the residuals are calculated using similar formulas. The most complete results are obtained for continued fractions on the set of quaternions. Bibliography: 20 titles.