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Number Systems Pertaining to Euclidean Rings of Imaginary Quadratic Integers

송현종|심효섭
영남수학회 (Youngnam Mathematical Society)|2015.05|East Asian Mathematical Journal|제31권 제3호|pp. 357-362|DOI http://dx.doi.org/10.7858/eamj.2015.027

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참고문헌

키워드

FractalsEuclidean ringsComplex base number systemsimaginary quadratic integers
주제분류수학

초록

For a ring R of imaginary quadratic integers, using a concept of a unitary number system in place of the Motzkin's universal side divisor, we show that the following statements are equivalent: (1) R is Euclidean. (2) R has a unitary number system. (3) R is norm-Euclidean. Through an application of the above theorem we see that R admits binary or ternary number systems if and only if R is Euclidean.

Abstract

For a ring R of imaginary quadratic integers, using a concept of a unitary number system in place of the Motzkin's universal side divisor, we show that the following statements are equivalent: (1) R is Euclidean. (2) R has a unitary number system. (3) R is norm-Euclidean. Through an application of the above theorem we see that R admits binary or ternary number systems if and only if R is Euclidean.

참고문헌 (19)

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관련 논문AI추천

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