Anti-integral extensions $ {R[{\alpha}]/R$

Main Article Content

Kiyoshi Baba
Ken-Ichi Yoshida

Abstract

Let $ R $ be an integral domain and $ \alpha $ an anti-integral element of degree $ d $ over $ R $. In the paper [3] we give a condition for $ \alpha^2-a$ to be a unit of $ R[\alpha] $. In this paper we will generalize the result to an arbitrary positive integer $n$ and give a condition, in terms of the ideal $ I_{[\alpha]}^{n}D(\sqrt[n]{a}) $ of $ R $, for $ \alpha^{n}-a$ to be a unit of $ R[\alpha] $.

Article Details

How to Cite
Baba, K., & Yoshida, K.-I. (2004). Anti-integral extensions $ {R[{\alpha}]/R$. Tamkang Journal of Mathematics, 35(1), 1–12. https://doi.org/10.5556/j.tkjm.35.2004.220
Section
Papers
Author Biographies

Kiyoshi Baba

Kiyoshi Baba, Department of Mathematics, Faculty of Education and Welfare Science, Oita University, Oita 870-1192, Japan.

Ken-Ichi Yoshida

Department of Applied Mathematics, Okayama University of Science, Ridai-cho 1-1, Okayama 700-0005, Japan.