논문KCI 등재
Unit groups of quotient rings of integers in some cubic fields
대한수학회 (The Korean Mathematical Society)|2017.10|대한수학회논문집 (Communications of the KMS)|제32권 제4호|pp. 789-803
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Let $K=\Q(\al)$ be a cubic field where $\al$ is an algebraic integer such that $\disc_K(\al)$ is square-free. In this paper we will classify the structure of the unit group of the quotient ring $\O_K/A$ for each non-zero ideal $A$ of $\O_K$.
Abstract
Let $K=\Q(\al)$ be a cubic field where $\al$ is an algebraic integer such that $\disc_K(\al)$ is square-free. In this paper we will classify the structure of the unit group of the quotient ring $\O_K/A$ for each non-zero ideal $A$ of $\O_K$.
참고문헌 (8)
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- D. M. Burton, "Elementary Number Theory" (1980), Allyn and Bacon, Inc.
- J. T. Cross, "The Euler Φ-function in the Gaussian integers", Amer. Math. Monthly, 90(8), pp.518~528 (1983)
- K. Ireland, "A Classical Introduction to Modern Number Theory" (1990), Springer-Verlag
- D. A. Marcus, "Number Fields" (1977), Springer-Verlag
- I. Niven, "An Introduction to the Theory of Numbers" (1993), John Wiley & Sons, Inc.
- A. Ranum, "The group of classes of congruent quadratic integers with respect to a com-posite ideal modulus", Trans. Amer. Math. Soc, 11(2), pp.172~198 (1910)
- P. Ribenboim, "Classic Theory of Algebraic Numbers" (2001), Springer-Verlag
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