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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2015.1
- 수록면
- 357 - 362 (6page)
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초록· 키워드
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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:
{\rm (1)} $R$ is Euclidean.
{\rm (2)} $R$ has a unitary number system.
{\rm (3)} $R$ is norm-Euclidean.
\noindent Through an application of the above theorem we see that $R$ admits binary or ternary number systems if and only if $R$ is Euclidean.
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참고문헌 (19)
참고문헌 신청
A. Petho / 1991 / On a polynomial transformation and its application to the construction of a public key cryptosystem, Computational Number Theory / Proc., Walter de Gruyter Publ.
D. Goffnet / 1991 / Number systems with a complex base: a fractal tool for teaching topology / Amer. Math. Monthly 98 (3) : 249255 ~
D.E. Knuth / 1960 / An Imaginary Number System / Communication of the ACM-3 (4)
H. J. Song / 1999 / Disclike Lattice Reptiles induced by Exact Polyominos / Fractals 7 (1) : 9 ~ 22
H.M. Stark / 1967 / A complete determination of the complex quadratic elds of class number one / Michigan Math. J 14 : 1 ~ 27
D. Goffnet / 1991 / Number systems with a complex base: a fractal tool for teaching topology / Amer. Math. Monthly 98 (3) : 249255 ~
D.E. Knuth / 1960 / An Imaginary Number System / Communication of the ACM-3 (4)
H. J. Song / 1999 / Disclike Lattice Reptiles induced by Exact Polyominos / Fractals 7 (1) : 9 ~ 22
H.M. Stark / 1967 / A complete determination of the complex quadratic elds of class number one / Michigan Math. J 14 : 1 ~ 27
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