Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2017; 32(4): 789-803

Online first article October 10, 2017      Printed October 31, 2017

https://doi.org/10.4134/CKMS.c160254

Copyright © The Korean Mathematical Society.

Unit groups of quotient rings of integers in some cubic fields

Ajchara Harnchoowong, Pitchayatak Ponrod

Chulalongkorn University, Chulalongkorn University

Abstract

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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 $\O_K$.

Keywords: unit group, quotient ring of integers, cubic field, square-free discriminant

MSC numbers: Primary 11R16

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